The 34-year-old Murray, given a wild card entry into the hard-court tournament, beat the 94th-ranked Kudla 6-3 6-2 in a match lasting just 69 minutes.
The Scot, currently ranked 109th, will now face a challenging second round match against Norwegian second seed Casper Ruud the world number 10.
Murray arrived in San Diego after reaching the quarter-finals at the Moselle Open in Metz last week, his best finish in seven tournaments since his latest comeback in June after lengthy spells in recent years due to hip surgery and a string of other injuries.
The former world number one had few problems dispensing with the 29-year-old Kudla, who gained entry as a lucky loser.
Murray won 90% of his first serve points compared with Kudla’s 63% and won 47% of his second serve points.
He also converted three of four break points against Kudla’s serve while not allowing his opponent a single break point over both sets
Murray’s last 16 match will be his first meeting with Ruud, who 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.