Coutinho, who completed his loan move from Barcelona on Monday, came on for an unhappy looking Thomas Müller with more than half an hour remaining, but had to be content with a co-starring role as Lewandowski stole the limelight.
The Polish striker opened the scoring with a penalty in the 20th minute, doubled Bayern's lead with a brilliant free kick in the 50th, and claimed his fifth league goal in two games with a fine turn and finish in the 75th.
Lewandowski also started the season with a goal in Bayern's 3-1 win over Energie Cottbus in the German Cup.
Schalke, playing its first Bundesliga game at home under new coach David Wagner, was left to rue two handball penalty decisions that seemed to go Bayern's way with minimal intervention from the VAR.