The 21-year-old, in her first appearance since a Wimbledon last-16 defeat earlier this month, won five straight games to take the first set but Mertens, the eighth-seeded Belgian, responded well to take the second set.
Having arrived on the east coast of the United States from the UK on Thursday, Raducanu was battling a five-hour time difference as the final set went past 11pm.
But the former US Open champion showed her mental resolve to win the last set, saving five break points at one point to overcome Mertens for the second this month following a win at Wimbledon.
“I was playing some pretty good tennis in patches throughout, especially in the first set and moments in the third set,” said Raducanu.
“I lost some focus in the second. It’s not easy playing at 11:30. I got here Thursday night so I’m still jet-lagged.
“I was telling myself, ‘I’m not leaving. This is not happening. You’re not losing this match’.”
Raducanu, who is still managing her return from ankle and wrist surgery, turned down the opportunity to play at the 2024 Olympics because she did not want to switch back to playing on clay ahead of the hard court season.