In a match of few chances, the Foxes did enough to nullify the home side and claim a result which ensures that they only require one more point to progress through to the knockout stages of the competition.
Leicester went into the game having impressed in their opening three group fixtures, but they produced one of their worst 45 minutes of the season in the first half as they failed to pose any threat to the Danish champions.
Towards the end of the first half, Leicester finally started to show some ambition in the final third but they were restricted to a long-range effort from Jeffrey Schlupp, which rolled through to the goalkeeper after a deflection off the ineffective Jamie Vardy.
Up the other end, Copenhagen were having the better of the ball in the final third but they, too, were restricted to efforts from outside of the penalty area.
The Copenhagen-born stopper also had to be alert to prevent the ball going in at the near post, but he was barely required on his return to Denmark until the final minute of the game.
A cross from Kasper Kusk found the head of Cornelius but despite his header seemingly destined for the bottom corner, Schmeichel got two hands in the way before Santander blazed the rebound over the crossbar.
With Leicester still needing to travel to Porto, it was an intervention that could make all the difference at the end of the group stages, and the Premier League champions will now hope to secure their place in the draw for the second round with a positive result against Club Brugge in three weeks' time.