The Eels produced a sloppy opening 40 minutes but kicked into action in the second spell to beat a much-improved Alhambra-Union 42-26.
Kaikorai's backline was too slick for a Pirates unit which continues to struggle on defence.
The midfield pairing of Jayden Spence and Danny van der Voort had acres of space to work as Kaikorai ran out winners 64-10.
University A bounced back from its defeat by Taieri last week with an impressive 35-10 win against Southern.
Dunedin pummelled an under-strength Zingari-Richmond side 79-7, while Harbour thumped Green Island 55-17.
Taieri 42
Alhambra-Union 26
Taieri retained the Speight's Challenge Shield but Alhambra-Union showed some fight.
Alhambra-Union has had a dreadful start to the season with a colossal defeat by University first up and a shock loss to Green Island last week.
But led by combative loosie Ben Webby, Alhambra had some good moments in the match.
It helped that Taieri put in an error-ridden opening 40 minutes and it was a mistake which led to the game's first points.
Alhambra-Union winger John Tapueluelu swooped on some loose ball and scampered 20m.
The cover defence got to him but he was able to reach out and plant the ball down in the corner.
Taieri lock Brendon Murdoch rumbled over in reply and the teams traded penalties to go to the the break locked at 11-11.
Taieri turned down an early handy penalty and it proved to be a good decision with Willis Scott driving off the back of a scrum and offloading to halfback Matt Ellis.
He got sandwiched but got the ball down.
Alhambra-Union halfback Caleb Gray ducked under a tackle and scored to keep his side in the hunt.
But the game-breaker started with Taieri fullback Mitchell Scott running the ball out from his own 22m.
He made his way up to the halfway then turned right and kept going. Matt Whaanga had cut in on an angled run and Scott found him with an inside ball.
Whaanga drew the last defender and passed to James Lentjes to finish.
University A 35
Southern 10
University A made an emphatic statement of its desire to go back-to-back as club champion with a clinical cleanout of Southern at Bathgate Park.
Both sides spent the first 15min locked in combat between the 10m marks until a series of penalties led to Southern's scoring machine, No8 Mika Mafi, diving over to score from broken play close to the line.
From the restart, University kicked into life and turned the ball over for left wing Taylor Haugh to score near the corner.
Throughout the second quarter, University A dominated in all facets and, in the best traditions of student rugby, ran Southern ragged.
Right wing Gavin Stark excelled on the dry ground and the up-tempo nature of the game, scoring two sensational tries, and setting up a second for Haugh, to begin the second half.
It was a sound all-round performance from Stark, who threatened with every touch, while proving an asset to his side's defensive screen.
Forced to feed on scraps of possession for most of the second half, the University forwards complemented some superb midfield defence, and were equal to the task of nullifying the threats posed by the big men of the Southern pack, allowing them little opportunity and effectively slowing ball clearance, which shut Southern out of the game.
Kaikorai 64
Pirates 10
One side did a lot of running.
The other side did barely any tackling.
Pirates struggled defensively last season and those gaps in the backline emerged again as Kaikorai ran in 10 tries at Forsyth Barr Stadium.
Midfield pairing Jayden Spence and Danny van der Voort had space to work in and the five-pointers kept coming.
It was rugged loose forward Blair Tweed who opened the scoring in the second minute when he burrowed his way over.
Van der Voort crossed four minutes later after he brushed aside some ineffectual tackles.
That moment perhaps summed up Pirates' afternoon better than any other.
Kaikorai had banked a bonus-point try before the break and led 29-5 at halftime.
Pirates' defence went missing early in the second spell and van der Voort strolled through another hole to score.
Highlanders back-up prop Craig Millar pegged a try back for Pirates.
His side had been battering away at the line for phase after phase and he eventually dived over untouched.
The floodgates opened after that.
Highlanders halfback Josh Renton scored a double.
The reliable Josh Clark was comfortably the best player for Pirates, while Tweed, van der Voort and No 8 Nathan Hull ran hard and created opportunities for Kaikorai.
Harbour 55
Green Island 17
Charles Elton's impressive work in the lineout paved the way for Harbour's eight-try 55-17 win over Green Island at Miller Park.
The No8 made 10 clean takes and was supported by flanker Ben Whale, as Harbourcontrolled possession.
The front row of Pete Mirrielees, Sekonaia T-Pole and Aiden Spence as Harbour pushed Green Island back in the scrum.
Spence used his strength to score a try after the Harbour pack won a tighthead close to the Green Island line. Mirrielees was strong on the drive and scored two tries.
Six of the Harbour tries were scored by the forwards, one of the best being the 40m run by towering lock Sione Misiloi early in the second spell.
Harbour scored four tries in the first spell and led 29-3 at the break. It added four more in the second spell.
Green Island had a short period of dominance when it scored two converted tries in the first 16 minutes of the second spell.
The best Harbour backs were first five-eighth Joe Collins, centre Aleki Morris and fullback Logan Allen, who kicked seven goals from nine attempts and scored 15 of his team's points.
For Green Island, rugged blindside flanker Jackson Hemopo got some go-forward and was backed up nicely in the second spell by replacement prop Ricky Hollamby and utility Simon Tupu.
Dunedin 79
Zingari-Richmond 7
Dunedin played into a solid wind in the first spell, played the possession game and spent the majority of the half camped deep in Zingari territory.
The pack dominated at scrum and lineout time.
It scored two tries from lineout drives to emphasise its dominance.
Dunedin winger Henry Scott provided the highlight of the spell when he received the ball out wide and from 55 metres went on an angled run, leaving half a dozen defenders in his wake and had the strength to reach out and score close to the posts.
Zingari-Richmond got its only points late in the half when winger Shaun Dungey went over it out wide.
Dunedin turned with the wind at its back and ran in eight tries from all over the paddock as the Zingari defensive screen collapsed completely.
Many of the tries were from long range, as once the first line was breached there was no cover and Dunedin ran in tries at will and with contemptuous ease.
For Dunedin, locks Alex Ainley, Mark Grieve-Dunn and, in the second spell, Harry Dodds, were prominent throughout and loose forward Hame Toma was at his bruising best.
Midfielders Tim Tolovae and Leroy Van Dam were constant threats to the defence and Henry Scott was a menace out wide.
For Zingari-Richmond halfback Maurice Stone and hooker Marcel Taani were its best.
