Lajovic secured a 6-4 7-5 win in one hour and 36 minutes.
Dallas Mavericks team governor Mark Cuban was left incensed after a bizarre incident and has vowed to protest Wednesday's loss as a result.
Ja Morant played for the first time since March 3, coming off the bench for 17 points and five assists as the Grizzlies beat the Rockets.
Dusan Lajovic was too good for Andy Murray despite a modest recent hard-court record, while Gael Monfils' injury problems re-surfaced.