Wawrinka, whose ranking has slumped to 225 after knee surgery, had lost his last four matches against Dimitrov, a semi-finalist in 2014.
But at the same tournament where he played what proved to be his last match of 2017, the 33-year-old was rejuvenated.
"It's a great feeling to win like this on Centre Court," said Wawrinka, twice a quarter-finalist at Wimbledon.
"I was moving well and feeling good.
"I knew it would be tough to beat a player like Grigor so my goal was to fight and focus."
Wawrinka will next face Italian qualifier Thomas Fabbiano.