Jamie Vardy, 33, became Leicester's oldest European scorer when he netted from the penalty spot after 18 minutes.
Hamza Choudhury then doubled the lead before half-time with an intelligent side-footed finish.
But the hosts got some hope early in the second stanza when Muamer Tankovic finished past Kasper Schmeichel.
Speaking after the game, Brendan Rodgers said: "It was very pleasing.
'It was a different type of performance. It was never going to be a fast-flowing game because the pitch was awful to be honest.
"It was a surface that the players didn't trust in their footing. It was very slippy. That aside, we took our chances in the first half. It was a really good move that led to the penalty and we go 1-0 up. Then we get the second.
"They came out at 2-0 down with nothing to lose and they got to 2-1. In any game, the momentum changes, and that's when we had to show our spirit. If you can't play the game you want with the ball, you can still defend really strongly and I thought we did that. We were calm to see the game out. It's a great result for us."