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.
Inter looked comfortable until Catania substitute Giuseppe Mascara set up a nervy finale by converting a penalty six minutes from time, given when Inter keeper Julio Cesar brought down Gianvito Plasmati after spilling a shot.
But the hosts held on for a triumph that gave them 22 points from nine games, two more than second-placed Sampdoria, who had briefly occupied the top spot by thrashing 10-man Bologna 4-1.
"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.
Reto Ziegler then drove in from outside the box before Mannini nodded in an Antonio Cassano cross to complete his double and make it 4-0 with just over a third of the match played.
Substitute Pablo Osvaldo took advantage of poor defending in the second half to pull one back for struggling Bologna, who had had striker Marco Di Vaio sent off for dissent after they went 3-0 down in their first match under new coach Franco Colomba.
