Lajovic shook off the loss of a first set tiebreak to dominate the second frame, earning two breaks of Isner’s fearsome serve.
However, trailing 6-5 in the final set and serving to stay in the match, Lajovic’s own serve failed him at the worst possible time as Isner, a finalist here in 2013, sealed the win to reach the second round.
Isner will next play either Spanish qualifier Pablo Carreno Busta or France’s Gilles Simon.
Also on Sunday, Australian Alex De Minaur rallied from a set down to beat Italian Marco Cecchinato 6-7(5) 6-1 6-2 and will next meet the winner of American Reilly Opelka and Borna Coric of Croatia.
“These wins are often the ones that count the most,” De Minaur, who did not drop a service game, told reporters. “To be able to come back from not playing my best tennis and turn it around, I’m really happy to get the win.”
Writing by Jahmal Corner in Los Angeles; Editing by Peter Rutherford