For the third time this term Leicester went into a Champions League game on the back of a heavy Premier League defeat but they shrugged off the disappointment to secure a third straight win in the competition thanks to Riyad Mahrez's 40th-minute goal.
It was no vintage show from Claudio Ranieri's men, who lost 3-0 at Chelsea on Saturday, although they were unfortunate not to triumph by a bigger margin after Islam Slimani had a goal harshly ruled out for offside in the second half.
They ended the contest, however, grateful to keeper Kasper Schmeichel for a superb one-handed save in the final minute as Leicester inflicted a first defeat on Copenhagen in 24 matches in all competitions.
The win moved Leicester onto nine points, one more than they have from eight games in the Premier League. With three matches remaining, they are five clear of second-placed Copenhagen and Porto, who beat Club Bruges 2-1 in Belgium.
For much of the encounter, especially the first half, Leicester looked exactly like a side struggling for points domestically.
They created little and struggled to get a stranglehold in midfield as their Danish opponents confidently stroked the ball around the pitch.
"It was a stern test that's for sure," said Leicester captain Wes Morgan. "We had to really work hard, be resilient and try to take our chance when it came."
When Leicester broke the deadlock five minutes before halftime, it was a goal out of nothing.
A deep cross from Jamie Vardy found Slimani lurking at the far post and he headed down for fellow Algerian Mahrez to flick the ball with the outside of his boot past Copenhagen keeper Robin Olsen and into the net.
The Danes were again the stronger side after the restart and did their best to peg the hosts back in their own half with Leicester enjoying only brief moments of relief before gradually gaining some momentum.
Mahrez slalomed into the area on 65 minutes before his weak effort was blocked, but Leicester did have the ball in the net moments later.
Their celebrations were swiftly curtailed by the lineman's flag, however, as Slimani was adjudged to have strayed offside before beating Olsen at the second attempt.
There were nervy moments for Leicester at the death, none more so than Schmeichel's superb save to deny Andreas Cornelius, palming his low effort away to safety from close range.
(Writing by Toby Davis; Editing by Tony Jimenez and Pritha Sarkar)
