On an evening when both sides struggled to convert chances McKenzie grabbed a last-gasp goal as Matt Baker failed to hold on to a Jim Brennan strike.
Dean Ashton was missing from the Norwich starting eleven, adding growing speculation over a move to West Ham or Manchester City, and the visitors lacked a killer instinct in the penalty area all evening.
Nigel Worthington's side travelled from Norfolk low on confidence following four matches without a win in the Championship, and had the first real chance of the game on four minutes as striker McKenzie shot wide from 18 yards.
The Dons are also yet to record their first victory of the new campaign but were boosted by the return of captain Ben Chorley after suspension.
Winger Jason Puncheon showed the most threat for the home side in the early stages as he saw a free-kick saved by Robert Green, before being denied again by the Norwich keeper moments later after a darting run.
There were few positives for either team to take from the opening 20 minutes as both sets of players gave the ball away regularly, but it was the home side who looked more threatening and Izale McLeod should have grabbed the first goal on the quarter hour mark - only to misplace his shot from six yards.
Norwich desperately lacked any spark with Ashton and Darren Huckerby missing, and Brennan was guilty of messing up a good chance after 30 minutes.
The midfielder cut in from the left and hit a low shot which was saved by Matt Baker, before McKenzie scuffed the rebound wide. If Brennan had passed instead of shooting the Canaries would surely have taken the lead.
The Dons were soon guilty of missing their own clear cut chance through Puncheon. A well worked move resulted in a superb cut back from the right by Wade Small, but Puncheon's first-time effort flew high over the bar.
After the break MK flew out of the traps as Green was forced to make a good stop from Small's effort. And Trent McClenahan saw his shot from distance hit the sidenetting.
Norwich struggled to find any rhythm throughout the game as the Dons began to take control and Nigel Worthington's team almost fell behind on 71 minutes only for Greth Edds drive to drift just over the bar.
Dons striker McLeod was stretchered off after landing awkwardly and as the game headed into the final five minutes both sets of fans desperately urged their side on to snatch a winner.
Small volleyed a right-footer wide before Norwich's Peter Thorne headed straight at Baker down the other end and the MK keeper pulled off another brilliant save from Thorne's follow-up effort.
Malvin Kamara came close with a header ten minutes into extra time but just failed to get enough on the ball from Clive Platt's cross. And on 105 minutes Kamara was brought down in the area by Jason Shackell - giving skipper Chorley a chance from the penalty spot.
However the Dons captain scooped his effort over the bar to give the Canaries a lifeline.
Gary Doherty and Small missed further chances as the match threatened to head to penalties, but McKenzie bundled home a last minute winner to end MK hopes of a giantkilling.