The Croat offered under pressure coach Felix Magath, the controversial former Schalke boss, some respite and lifted Wolfsburg to six points from five games.
Spaniard Raul - who was Magath's biggest transfer coup at Schalke last year - needed only 13 minutes to strike, volleying in a clever chip from Peruvian Jefferson Farfan to put the visitors in the driving seat.
Wolfsburg quickly recovered and levelled with Mandzukic heading in from close-range after being left completely unmarked.
With Schalke offering little further threat, the hosts gradually grabbed the initiative in the second half and snatched the lead when the Croatia international deflected a Marcel Schaefer free-kick into the net.
Schalke missed the chance to join leaders Bayern and Werder Bremen on 12 points, remaining stuck on nine.
Bayern lead the table following their 7-0 demolition of Freiburg on Saturday with Mario Gomez netting four times. Bremen are second on goal difference after their 2-0 win over rivals Hamburg SV.
Also on Saturday, Borussia Monchengladbach kept up their fine start to the season with a 1-0 win over Kaiserslautern that lifted them to third place on 10 points.
In the only other Sunday game, visitors Nuremberg scored twice from the spot through captain Timmy Simons in a span of four minutes to secure a 2-1 win at Cologne.
In a rugged and at times bad-tempered encounter that left both teams with 10 players, Cologne cut the deficit just before the break through Adil Chihi but could not find the equaliser despite pressing for most of the second half.
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