The 87th ranked Thompson beat the world number three 7-6(0) 4-6 7-6(5) for his second career win over a top 10 player and first against the Greek in three meetings.
Thompson struggled out of the gate when he fell in the first round of January's Australian Open and suffered early exits in Dallas and Delray in February.
To reset he entered an ATP Challenger event in Georgia that he won without dropping a set and rode that momentum into Indian Wells, where he backed up his straight sets first round win over Frenchman Gael Monfils by toppling Tsitsipas.
"A little bit of a slow start to the year," Thompson told reporters.
"Won a Challenger couple weeks ago and it was good to get those matches under my belt. I came here and got a tricky draw but have come through it.
"I think playing a lot of matches helped. I just felt comfortable on the match court and got match fit."
Thompson held his nerve in the tight third set and embraced the moment when Tsitsipas waved his arms up and down to rally his supporters ahead of the deciding tiebreaker on center court.
"I actually started laughing when he was doing that," he said.
"Not that it was funny that he was doing it but because I want to be in these positions. I'm enjoying the battle."
Next up for the man from Sydney is a third-round clash against Chilean qualifier Alejandro Tabilot.
