The Suns were down one with 0.9 seconds left when Crowder lofted a high pass on an out-of-bounds play on the baseline. A soaring Ayton came down the lane and stuffed it through the net over L.A.'s Ivica Zubac as the crowd roared in disbelief at Phoenix Suns Arena.
The referees spent about a minute reviewing the play before ruling the basket was good. The Clippers couldn't get a shot off in the final 0.7 seconds.
The Suns now have a 2-0 lead in the series heading to Los Angeles for Game 3 on Thursday night. The Clippers will be fighting from a 2-0 deficit for the third time in these playoffs after rallying to beat the Mavericks and Jazz in the first two rounds.
The Crowder-to-Ayton connection negated a Clippers rally that was led by Paul George, who had 26 points.
George made a layup with 31 seconds left to give the Clippers a 101-100 lead for their first advantage since early in the third quarter. Suns guard Devin Booker responded with a jumper of his own with 27 seconds left.
George calmly took the ball on the next possession and drilled a long two-pointer for a 103-102 lead.
But there was a lot more action left.
George missed two free throws with 8.2 seconds remaining and the Suns had a chance to win, but it looked as if it wouldn't happen when Mikal Bridges missed a corner 3-pointer and the ball was deflected out of bounds.
Instead, it set up Crowder's heave to Ayton, who was dominant in the paint all night.
The Suns have won nine straight in the playoffs, which is a franchise record.
The Suns were led by Cameron Payne, who was brilliant while subbing for All-Star Chris Paul. He finished with a career-high 29 points. Ayton had 22 points and 14 rebounds, while Booker added 20 points.
Payne repeatedly carved through the Clippers defense, making tough buckets at the rim with pretty left-handed finishes. He made what looked like a crucial layup with about 90 seconds left, finishing high off the glass to give the Suns a 100-95 lead.
But the gritty Clippers responded and nearly pulled this one out.
It was a tough night for the stars from Game 1 until the final minutes. Booker shot just 5 of 16 from the field and missed part of the third quarter with a bloody nose. George was 10 of 23 from the field and missed his first seven 3-point attempts before his late buckets.
Ayton continued his eye-opening performance in these playoffs. The No. 1 overall pick in 2018 out of Arizona often has been overshadowed by later picks in the same draft like Atlanta's Trae Young and Dallas' Luka Doncic. But he has carved out quite a niche in Phoenix and now has a play that will live in franchise lore.