Pique had been shown a second yellow for a handball just before the break. The central defender instinctively bundled the ball into the Olympiakos goal with his forearm when Gerard Deulofeu's shot was parried into his path five yards out.
Shinji Okazaki's header and instinctive strike put Leicester in control, but Gary Cahill nodded in before the break. Cesar Azpilicueta equalised with a long-range strike before Foxes defender Marcin Wasilewski was sent off.
It had taken Sevilla just five minutes to take the lead as Wissam Ben Yedder tapped in from close range after home defender Dejan Lovren fell over while trying to clear the ball.
Defender Dani Carvajal scored a fine solo goal a minute from the end of extra time as Real Madrid beat Spanish rivals Sevilla in a dramatic UEFA Super Cup.
Kalvin Phillips made another error for the third goal. West Ham had 20 shots and might have equalised just before Garnacho's first had Emerson Palmieri capitalised on an error by Harry Maguire on the England defender's return to the team.
Chelsea defender Gary Cahill celebrated his return to England's squad and stepped up his claims for a starting place against Tunisia in Volgograd on 18 June by opening the scoring with a powerful header after only seven minutes.
And in the 71st minute Kevin De Bruyne played a sublime cross-field pass to Sterling who pushed the ball past defender Nacho Monreal and finished low beyond the Arsenal goalkeeper.
Aymeric Laporte's second league goal of the season put City ahead in the final moments of the first half, Everton giving thedefenderthe freedom of the penalty area to head past Jordan Pickford.
Belgium, England's Group G opponents, were again without injured defender Vincent Kompany in Brussels, while Eden Hazard limped off in the 70th minute.
The Spain striker took advantage of a mistake by a hesitant Gareth McAuley in the 76th minute to rob thedefender of possession and curl a brilliant left-foot shot past Ben Foster.
Senegal have to go without man-mountain defender Kalidou Koulibaly tonight due to suspension - will that have an impact? Follow all the action, as it happens, right here...