The reigning champions recorded their first Bundesliga victory since October 27 thanks mainly to Serge Gnabry, who scored both goals for the visitors against his former club on Saturday.
Bayern could have scored more in a game they dominated for long periods, yet their profligacy in front of goal kept Bremen – who had defender Niklas Moisander sent off in stoppage time – in the contest right through to the final whistle.
Still, a 16th straight league triumph over their opponents rounded out a good week for Kovac, with Bayern having clinched a place in the Champions League knockout stages with a 5-1 thrashing of Benfica on Tuesday.
Kovac praised his team's overall performance, but did take issue with their inefficiency in front of goal.
"My team turned in an exceptionally good display," the Croatian told the club's website. "We dominated the match technically, tactically but towards the end also in terms of fighting spirit. We did a really good job today.
"If there's something I find fault with, it's our conversion of chances. I counted six, seven more gilt-edged chances we should have converted into goals.
"But I liked it that way – without the ball we all defended together, with quick turnovers. You saw we had space and could make use of our quality up front.
"I'd like to congratulate my team on the performance."
"This victory brings a lot of relief and creates self-confidence. Today we did not allow much," the Germany international said.
"Of course we know about the situation in the table, so three points are always important. I'm overjoyed with my two goals today and that I could help the team win."
Kovac had Kingsley Coman and Thiago Alcantara available again, with the former making his first league appearance since the opening day of the campaign when replacing Franck Ribery in the first half.
Gnabry – who was also back in action after missing Bayern's last two games – welcomed the return of the duo, adding further depth to a squad that has been beset by injuries this season.
"We are well-staffed and need all the players. It's good that the competition [within the squad] is getting better again," he added.