The 2013 omnium world champion, was fourth after the opening three events of the six-discipline event.
He was fourth in the individual pursuit in 4min 29.953sec and seventh in the scratch race. Gate pushed hard in the elimination but was brought down in a crash, recovering before he was eliminated in seventh place.
Colombia's Fernando Gaviria Rendon was leading on 110 points and Gate was fourth on 88.
Raquel Sheath, who rode in two rounds of the team pursuit on Saturday, found the competition challenging yesterday.
The Waikato rider was 16th in the individual pursuit, 18th in the scratch race and 12th in the elimination, to be 16th overall.
Earlier, Eddie Dawkins and Matt Archibald placed second in their heats of the keirin, with Dawkins winning his repechage to advance to the second round. However, he was fourth in his second-round race and was eliminated. Archibald missed out in the repechage.
Stephanie McKenzie qualified for the elimination rounds of the women's sprint, clocking 11.406sec to be 20th in the qualifying. McKenzie lost her first round of elimination to Hong Kong's Wai Sze Lee.
In a non-world cup race, Westley Gough and Pieter Bulling were fourth in the men's madison.
On Saturday, New Zealand claimed silver and bronze medals on the opening day of the event.
The men's team pursuit took an outstanding silver medal and excellent qualifying points, which should cement its spot for February's world championships.
The world champion men's team sprint claimed the bronze medal, as it did in the opening world cup last month. The New Zealanders were pipped by just 0.007sec for a placein the final, finishing third-fastest in an extraordinary qualifying session where 0.2sec separated the top four teams.
Germany led the way with 43.700sec on a sluggish London velodrome, Australia was second in 43.832sec and New Zealand posted 43.839sec.
The Kiwi combination of Ethan Mitchell, Sam Webster and Eddie Dawkins then edged the French, the former world champions, in the ride for the bronze, clocking 43.713sec. Germany was fractionally faster than New Zealand in claiming the gold medal over Australia.
In both team pursuits, the New Zealand coaches opted to use their specialist omnium riders, Aaron Gate and Raquel Sheath respectively, for the qualifying, resting Myron Simpson and Jaime Nielsen. They came back into the team for the second ride, to add a fresh boost in the exhausting three rides on the opening day.
The men's combination of Gate, Pieter Bulling, Westley Gough, Cam Karwowski clocked a solid 4min 3.773sec to be fourth fastest, 3sec behind top-ranked Australia and only narrowly behind host Great Britain and Denmark.
New Zealand drew Australia in the semifinal, with the Australians, who went down to three riders for their final push, having Luke Davison puncture and fail to finish.
The New Zealanders took full advantage to claim the win and move to the gold medal ride, relegating the Australians to the ride for seventh and eighth.
The Kiwis pushed hard to match Great Britain until the midway mark of the 4000m final but ran out of gas and had to settle for second.
The New Zealand women were seventh-fastest in London but dominated their first round clash against Germany, winning by more than 3sec.
The Germans' time was the second quickest of the other teams, which meant a repeat race for fifth and sixth. The New Zealanders started well but both teams remained locked for the next 2000m before the Germans were the first to blink, edged by 0.3sec at the finish.
Great Britain came back from a slow start to win the final over Australia and Canada was third.
The women's team sprint combination of Katie Schofield and Stephanie McKenzie were 10th-fastest in 34.111sec from the 22 teams, just over a second behind leader China.
