The Stockholm side moved up to fourth place in Allsvenskan, leapfrogging third-placed Häcken in the fight for a European place. They are two points ahead of Djurgården, who also have one game in hand.
Top scorer Kristian Lien showed the way for Djurgården when he headed in the opening goal in the 35th minute after a quick counterattack in which Piotr Johansson's cross was perfect.
It was Lien's 12th goal of the season.
Malmö had a lot of the ball before the break, but did not create much.
Instead, it was Djurgården, heavily criticised after the derby loss to AIK last weekend, who were on the attack.
Under-pressure coach Jani Honkavaara saw both Lien and Patric Åslund miss chances to extend the lead early in the second half before Jeppe Okkels scored the 2-0 goal in the 58th minute.
Åslund then made up for his miss when he made it 3-0 with eight minutes left in regular time.
"We haven't come up to par in the last two games, we're a little sharper today, everyone works for each other and we're a damn good team," Johansson says.
Malmö had the same number of points as Djurgården before Monday night's meeting, but MFF's lacklustre performance led to a third straight home loss and the gap to the top three remains five points.
MFF's loss was the eighth of the season - six of them have come at home - and the big club, with nine Swedish championship titles since 2010, is only seventh.
