Defending champion and fifth-seeded Marin Cilic of Croatia saved a match point and swept the last five games to down Spanish qualifier Feliciano Lopez 4-6, 7-6 (5) 7-5.
Also winning were second-seeded Tomas Berdych of the Czech Republic, No. 3 Juan Martin del Potro of Argentina and No. 4 Jo-Wilfried Tsonga of France. But No. 6 Sam Querrey, the 2010 champion, was ousted by former four-time tournament winner Lleyton Hewitt, who won 5-7, 6-3, 6-4.
Murray resumed his match against Mahut at 2-2 in the second set and fought off three break points in his first two service games before beating the Frenchman in the tiebreaker.
The top-seeded Scot then took charge early against Matosevic, breaking the Australian to lead 2-1 and again in the fifth game. A break for 1-0 gave Murray a perfect start to the second set and a further break for 4-1 all but sealed his opponent's fate.
''The hardest part is just the waiting around,'' Murray said. ''We came off maybe three times yesterday. Today, the same thing again, a lot of waiting around for my match this afternoon. It's important to make sure you sort of relax and don't waste too much energy between matches.''
Berdych eased past 16th-seeded Grega Zemlja of Slovenia 6-3, 6-4, and Del Potro surrendered just eight points in the opening set against Britain's Daniel Evans before winning 6-0, 6-3.
Tsonga, the runner-up to Murray in 2011, survived two three-set battles. He defeated fellow Frenchman Edouard Roger-Vasselin 6-3, 6-7 (2), 6-3 in a rain-delayed second-round match and then Dutchman Igor Sijsling 7-5, 5-7, 6-3.
American Denis Kudla reached his first ATP Tour quarterfinal with a 6-1, 6-3 win over Kenny De Schepper of France, and Benjamin Becker of Germany upset seventh-seeded Alexandr Dolgopolov of Ukraine 7-6 (5), 7-5.