Ghana midfielder Muntari - who has been linked with a move to Tottenham Hotspur in recent weeks - put the champions in front on 13 minutes when his lob into the box towards Samuel Eto'o was allowed to bounce into goal as Catania keeper Andrea Campagnolo stood motionless.
Dutchman Sneijder curled in a splendid right-footed free kick to double the lead just past the half hour mark shortly after Patrick Vieira had thrashed the ball against the bar from short range.
"I'm happy with how we played in the first half and how we fought in the second," Inter boss Jose Mourinho, whose side's winless run in the Champions League continued with a 2-2 draw with Dynamo Kiev on Wednesday, told Sky television.
"It's never easy after a Champions League match. I changed a few players. We had some chances to close the match which we didn't take and then everything changed with their goal.
"It gave Catania hope, put us under pressure and the result was in doubt until the end."
Samp forward Giampaolo Pazzini, wearing a face mask after breaking his nose in last weekend's 1-1 draw at Lazio, touched in to give his side an early lead before midfielder Daniele Mannini volleyed home the second in the 17th minute.
