It was the fourth time out of the five games they've played this season that the Jets and Avalanche couldn't settle it in regulation time.
Winnipeg is desperately trying to gain enough ground to claim a wild-card playoff spot in the Western Conference.
They went into the third period tied 3-3.
Ladd's second came on a power play at 4:58 when he was poised near the inside edge of the faceoff circle and caught Wheeler's pass from the boards.
But Mcleod scored his third goal of the season on Montoya when he got a little one-on-one time to tie it up again at 10:23.
Wheeler ended it at 1:42 of overtime with a shot from near the boards that slashed through traffic.
O'Reilly's first goal came just 20 seconds into the game on a sharp-angled shot that slipped past Al Montoya but the Jets responded with serious pressure.
They had four shots to Colorado's two as Ladd evened things up at 3:15 with his 20th of the season, racing in on Reto Berra's stick side. It was Berra's first start since he was acquired by Colorado from the Calgary Flames at the trade deadline.
Tangradi put the Jets ahead with his first goal since November and only second of the season as Wheeler swept around the Colorado net, slipped the puck across the crease and Berra didn't even have time to react before it was over the line.
Colorado came back with several good chances but it wasn't until 17:47 that Landeskog shovelled in Andre Benoit's rebound to tie the game going into the second period and they outshot the Jets 12-8 in the first.
The second period was all Jets. They had outshot the tired-looking Avalanche 8-1 with Kane's goal at 12:02 as he snapped one from the netside of the left faceoff circle.
But some weak defensive play in their own end in the final minutes finally cost the Jets as Holden flipped a soft one in at 19:29, although Winnipeg outshot Colorado 11-5 in the second period.
Notes: Despite the disparity in their NHL rankings, the Jets and Avalanche went into Wednesday's game with two wins each in their season series, although Colorado had the only win in regulation time. Even the regulation win was decided by one goal.