Djokovic enjoyed a 6-4 6-4 win over Canada's Vasek Pospisil while Murray was even more ruthless as he tamed 13th seed Lucas Pouille 6-1 6-3.
Simon, ranked 32nd in the world, took 96 minutes to beat U.S. Open champion Wawrinka and set up a last eight clash with American Jack Sock, who humbled fifth seed Milos Raonic 0-6 6-4 7-6(8).
The Swiss was leading 3-1 in the first set but a flurry of unforced errors allowed Simon to finish off the upset victory.
Djokovic opened up a 4-0 lead in the first set as Pospisil mounted a spirited comeback by breaking back in the sixth game. However, the Canadian could not stop the Serbian from wrapping up the set.
Even though Pospisil fired 12 aces and 28 winners, he was no match for Djokovic, who has not dropped a set this week after withdrawing from last week's China Open with an elbow problem.
Defending champion Djokovic will face unseeded German Mischa Zverev, who battled past Spain's Marcel Granollers 6-7(4) 6-4 6-1, for a place in the semi-finals.
"I thought it was a great quality of tennis today from both players. I was very pleased with the way I played from the first to last point. I don't think I dropped my level at all," Djokovic told the ATP website (www.atpworldtour.com).
Murray, who captured the China Open last week, won the first five games of the match and broke in the first game of the second to send Frenchman Pouille packing.
The Scot will next face Belgium's David Goffin, who came from a set down to defeat sixth seed Gael Monfils 4-6 6-4 6-2.
Frenchman Jo-Wilfried Tsonga downed Alexander Zverev 6-7(4) 6-2 7-5.
(Reporting by Ian Rodricks in Bengaluru, editing by Pritha Sarkar)
