The Dutch midfielder, signed from Real Madrid at the end of the transfer window, curled the ball in from a tight angle to send Jose Mourinho dancing down the San Siro touchline and put his side top of the table after seven matches.
"It's a goal the team deserved. In the end we've played a great game against a great side," Mourinho told Sky television.
Dejan Stankovic shrugged off a back injury to give hosts Inter the lead midway through an entertaining first half when he ran on to Samuel Eto'o's pass and rifled the ball into the top corner.
The Serb, who grabbed the equaliser in the 1-1 draw at Rubin Kazan in the Champions League in midweek, later went close with two other efforts but by then Inter had already been pegged back.
Serie A top scorer Antonio Di Natale bagged his ninth goal of the campaign on 27 minutes when Cristian Chivu played the Udinese striker onside and he calmly fired home.
Di Natale is likely to be named in Italy's squad on Sunday for the forthcoming World Cup qualifiers against Ireland and Cyprus.
However, Inter striker Diego Milito looks doubtful for struggling Argentina's qualifiers against Peru and Uruguay after going off with a hamstring problem early on.
His replacement Mario Balotelli, who angered Mourinho when sent off against Rubin, was again frustrating with Inter showing the same weaknesses as in last weekend's 1-0 defeat at Sampdoria.
Possession was often wasted in a scrappy second half and gaps were left at the back with the splendid Di Natale having two other good chances.
Sneijder had the last laugh, though, after Inter increased the tempo in the closing stages.
Sampdoria can return to the top with victory over Parma on Sunday before third-placed Juventus visit Palermo.
Bari drew 0-0 at home to struggling Catania in Saturday's other game with the hosts going closest when Vitali Kutuzov hit the post after a mistake by goalkeeper Mariano Andujar.
Promoted Bari, whose takeover by an American property tycoon collapsed during the week, had already drawn with Inter and AC Milan this term.
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