Three months on from a humiliating 4-0 home loss to Armenia in their last Group B outing, Morten Olsen's men again looked far from assured and needed a 53rd-minute own goal from Ryan Camilleri to seal a nervy win.
Denmark had earlier taken the lead inside 90 seconds through Leon Andreasen, but group minnows Malta levelled through Clayton Failla's wonderful free-kick seven minutes before the interval and Denmark struggled to assert themselves in the second period.
The Danes will need to raise their game if they are to exact revenge on Armenia - with whom they are now level on nine points - when they meet for their return fixture in Yerevan on Tuesday.
The pain of June's mauling at Armenia's hands has been felt by the Danes all summer, and they wasted no time in venting their frustration tonight as they took the lead with just over a minute on the clock when Martin Braithwaite crossed and Andreasen steered home into the bottom-left corner.
The warning signs were there for the fragile Danes and Malta duly broke through in the 37th minute when Failla curled home a fine free-kick from 25 yards.
Malta went close to taking the lead five minutes into the second half but Michael Mifsud's header came back off the crossbar.
And within three minutes Denmark profited from their fortune to retake the lead. Tottenham new-boy Christian Eriksen ran at the home defence and hit a rising shot that came down off the crossbar before being turned into the net off Camilleri, who was attempting to clear the danger.
Andreasen and Eriksen tested home goalkeeper Justin Haber in what time remained, but Malta were never out of it and will feel aggrieved to go away with nothing to show for their efforts.