The Bavarians have now won the German league title a record 29 times.
Midfielder Dani Ceballos added: "It looks like us changing our coach worked. We have recovered some sensations we had lost and we have got the three points. Now our objective is to win all the games left and finish the season as well as possible."
The United fans, who celebrated the victory at the end of the game with the manager and players, have not been the source of criticism of Solskjaer -- indeed the Norwegian has enjoyed strong backing from supporters who attend games at Old Trafford and those who travel away.
Images from the UEFA Champions League matches played on Tuesday.
In Pep Guardiola's 100th match in charge of the Manchester club, captain De Bruyne led from the front as City outclassed the Gunners, who have now suffered six home games without a win. Images from the EPL matches played on Sunday.
Images from the Euro 2020 qualifying matches played on Tuesday night.
News of all that's transpired on and off the football field
Barcelona forward Ousmane Dembele scored twice and produced a mesmerising display to fire his side to a 5-1 win over Villarreal on Wednesday which stretched the champions' unbeaten run this season to 36 games with two remaining.
Liverpool had won each of their previous four home leagues games in which they conceded first and 12 minutes later they had turned another match on its head as Roberto Firmino's trickery set up Mane to give the hosts the lead at the second attempt.
A round-up of Tuesday night's matches in the UEFA Champions League.
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