Evans battled valiantly in tough conditions in an attempt to avoid falling out of form this season and drop out of the world's top 200.
Kachanov threatened to go 5-0 up in the decider, stopping three break points to cut the deficit to 4-3.
Evans fed off the support of the raucous crowd to secure a victory that will live long in the memory.
“I felt a little sorry for myself, but I didn't want to go out of another Slam with a fight and a whimper because I quit,” Evans said after the win, his first in a major this year.
“I could see him struggling a little bit and trying to take it one game at a time.”
Each set lasted over an hour, with long games and several break opportunities.
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Set 1 – 68 minutes
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Set 2 – 67 minutes
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Set 3 – 72 minutes
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Set 4 – 67 minutes
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Set 5 – 61 minutes
With both players holding their breath, Evans cruised to victory, breaking the previous US Open record — set by Stefan Edberg and Michael Chang in the 1992 semifinals — by nine minutes.
Evans endured a tough year, winning four ATP Tour matches heading into the final Grand Slam of the season.
That poor form, coupled with a decision not to defend the title – and ranking points – he won in Washington last year to play doubles with Olympic-retiring Andy Murray, knocked Evans into the world's top 175.
Beating Kachanov was a reward for his persistence — and for Murray, his generosity.
“I had a terrible year. I knew I did the work, but not enough because I was injured a little bit,” Evans added.
“I like to think I got lucky in the end [against Khachanov]. I almost blew it but I'm so happy.
“It was amazing at 4-2 and it really started to go. I don't know how many Brits were there but the whole place seemed to want me to win.”
Evans has 48 hours to recover before playing Argentina's Mariano Navon in the second round on Thursday.