Andy Murray won his first match 6-3 6-2 in the San Diego Open after a late replacement saw him face lucky loser Denis Kudla.
The 34-year-old former world number one was set to face Japan's Kei Nishikori, who withdrew with a back injury.
Cameron Norrie also had a straight sets win in the first round over Germany's Dominik Koepfer 6-2 7-5.
British number one Dan Evans is in action on Wednesday and he faces South African lucky loser Kevin Anderson.
Wildcard Murray cruised through his match against the 29-year-old American in just 69 minutes but is likely to face more of a challenge in the second round against the Norwegian second seed, Casper Ruud, ranked world number 10.
Murray, currently ranked 109 in the world, reached the quarter-finals at the Moselle Open in Metz last week. That was his best finish in seven tournaments since his latest comeback in June after four disrupted years following a major hip injury.
"First and foremost it's great to be on the court healthy and competing week after week for the first time since 2017. It's been a long time and I'm starting to feel better with each match," he said in his on court interview.
Ruud has been in strong form this year with tournament wins on clay in Geneva, Bastad, Gstaad and Kitzbuhel, with his world ranking rising from 27th in January to his current place in the top 10.
Norrie will face the winner of the clash between Evans and Anderson.
In the WTA Chicago Fall Tennis Classic tournament, Harriet Dart made use of her lucky loser position in the main draw to beat Brazilian qualifier Beatriz Haddad-Maia 6-1 3-6 6-1.
She will face the Russian 12th seed Veronika Kudermetova.