"Their motivation is now bigger because of that and they will prove it on the pitch", Lewandowski, who scored twice to become the league's all-time foreign scorer, said after their big win.
"We could and should have scored more goals".
Their goal spree was enough to move top on goal difference above long-term leaders Borussia Dortmund, who beat Stuttgart 3-1.
Having been told on Tuesday, along with Bayern team-mates Jerome Boateng and Mats Hummels, that his Germany career is over, Mueller took out his frustration, setting up the first goal and scoring Munich's second.
Kimmich scored with a header on 82 minutes and Lewandowski claimed his second by guiding his header into the far corner three minutes later.
The Poland forward also took his tally against Wolfsburg to 20 goals in 17 matches.
"We are now where we want to be - first in the table and that's where we want to stay", added Kovac with nine rounds of league games left.
Koen Casteels saved from Lewandowski and Gnabry, who opened the scoring in the 34th minute as he stabbed in Muller's low cross.
But Stuttgart levelled with Marc-Oliver Kempf in the 71st before Alcacer notched his 14th goal of the season.
It was also the 12th consecutive defeat for Wolfsburg coach Bruno Labbadia against Bayern, more than any other coach against a single opponent.
Despite some dogged Stuttgart defending, Dortmund took the lead at Signal Iduna Park when Reus netted a penalty on 62 minutes. Lucien Favre's side handed out a 4-0 thrashing to Atletico Madrid when few expected them to win earlier this season.
Third placed Leipzig played out a goalless stalemate with Augsburg, and Borussia Monchengladbach returned to winning ways after beating Mainz 1-0.