So long did the forward need attention on a shoulder injury late in the game that referee Bobby Madden elected to add on five minutes beyond the conventional 90 to make up for lost time.
McKenzie had departed on a stretcher but his team ensured some good would come from their player's suffering when Craig Slater scored deep in that injury time to earn the Ayrshire side a precious victory.
This was Kilmarnock's first win away from home against top-six opposition and they sealed it in some style. Slater took possession around the halfway line and just kept running before unleashing a shot that sped past Gunnar Nielsen. It was the 19-year-old's first senior goal.
As well as clinching a victory that lifted Kilmarnock five points clear of the relegation play-off place, Slater's timely intervention also got team-mate Alexei Eremenko off the hook.
The flamboyant Finn had passed up a glaring opportunity to score just minutes earlier, electing to chip Nielsen when clear in on goal rather than simply putting his laces through it, with the ball bouncing off the top of the crossbar.
"It just shows you how good he is that he even tried it in the first place," said Rugby Park manager Allan Johnston. "But we showed our character by going straight back up the park and getting the winner."
The only sour note, then, on an otherwise good day for Kilmarnock was the injury sustained by striker McKenzie. "It looked a sore one so we'll have to wait until it's settled down," added the manager. "He hurt his shoulder with the way he landed."
This was a day when Motherwell's luck finally ran out. They had won their two previous matches without being at the top of their game but on this occasion fortune favoured the opposition, with manager Stuart McCall cursing the uneven Fir Park turf for its role in Slater's winner.
"They caught us on the break and it was a decent effort from Slater but Gunnar was saving it until it took a bobble," he said. "It's just a little bit of bad luck that we didn't need."
Motherwell had gone in front just before half-time, Iain Vigurs lashing a shot past Craig Samson from the edge of the box. Vigurs could have had a second before the interval, an exquisite turn creating space for a shot that whooshed into the side netting, befuddling some in the Main Stand who mistakenly cheered for a goal.
Had he scored, it would have been rough on a Kilmarnock side that had contributed plenty to an open game but had failed to take their chances early on. Robbie Muirhead powered in a fierce shot that Nielsen did well to parry, before repelling another attempt by McKenzie.
Motherwell had opportunities of their own. John Sutton's thrash from a free-kick beat the wall but not the diving Samson and Craig Reid was unable to convert the rebound. Reid then had his goalbound header booted off the line by Muirhead.
It was Kilmarnock, however, who would claim the next goal, with Jackson Irvine allowed to amble forward unfettered before threading a pass through to McKenzie who finished well.
Motherwell could have gone back in front, but Vigurs' free-kick was pushed back out by Samson and neither Zaine Francis-Angol nor Sutton could touch in the rebound.
It was left to Slater to win it late on for Kilmarnock - with a little inadvertent help from McKenzie.