The Wells XI was dismissed for 177 in reply to the Cumming XI's first-innings total of 255 for nine and trails by 203 runs after the Cumming XI reached 125 for four by stumps in its second dig.
Fast bowlers James McMillan and Mat Harvie impressed in grabbing two wickets apiece, and off-spinner Nathan McCullum, fresh from scoring a century on Tuesday, took two for 38 from 15 overs.
Jordan Sheed top-scored for the Wells XI with 38 and Sean Eathorne and Anthony Bullick both chipped in with 20.
Bullick was the pick of the Wells XI bowlers, taking two for 21.
He dismissed Leighton Morgan for 46 after he got a delivery to rise on the batsman and had him caught at forward square leg.
He also trapped in-form left-hand batsman Greg Todd lbw for 52.
Spinners Will Somerville and Nick Beard bowled well in tandem without success.
Barring weather intervention, Auckland will beat Canterbury in the first State Championship match of the season.
Although the four-day game will go to its final day in Rangiora today, the defending champion has no hope of salvaging a draw, with a late-afternoon batting collapse leaving it 280 for nine in its chase for 405 to win.
Corey Anderson (39 not out) battled resolutely with No 11 Hamish Bennett to delay the inevitable, aided by bad light halting play shortly after 6.15pm.
Rookie leg-spinner Tarun Nethula effectively ended Canterbury's last real chance of chasing down the runs when he floated in a tempter to New Zealand squad member Peter Fulton and Scott Styris latched on to the catch in the slips to break a 99-run third-wicket partnership.
Fulton (64) and Johann Myburgh came together when Canterbury was teetering on 79 for two and took the side 148 for two at lunch.
But once Nethula dislodged Fulton with the score on 178, Canterbury looked vulnerable and when Myburgh (67) went, there was little resistance left.
For Auckland, Colin de Grandhomme took three for 37, while Nethula bagged three for 71.
