The 20-year-old struck in the 74th minute to earn the Wolves all three points and take them five points clear of the bottom three, leaving Stuttgart without a win in their last four games of 2011.
The visitors only have themselves to blame for not reversing their recent slide as they missed several good chances early on, but there was only one team in it once Polter scored.
A bit more of a striker's instinct could have enabled Martin Harnik to give Stuttgart the lead, but he instead tried to provide Christian Gentner with an easy chance to score when he only had Diego Benaglio to beat in the 14th minute, but his pass was behind his team-mate.
Gentner, who put Stuttgart ahead against Bayern Munich last weekend, nearly repeated that feat two minutes later, but he headed over from a corner.
The visitors were getting closer to scoring, though, and Harnik spurned another great opportunity when put through on goal again in the 18th minute.
This time he had no other choice to go it alone but his self-confidence was lacking and he wasted the opportunity.
Wolfsburg's first chance arrived in the 25th minute, but Stuttgart goalkeeper Sven Ulreich was alert to the danger and tipped Ashkan Dejagah's deflected shot over the crossbar.
Another good reaction from the otherwise-untested Stuttgart goalkeeper prevented Alexander Madlung from heading the Wolves in front just before the break while Madlung then missed an even better chance, shooting wide of an open goal, much to Ulreich's relief.
Ulreich was much busier in the second half, although there was nothing he could do to prevent Polter from putting Wolfsburg ahead in the 74th minute.
He met Marcel Schafer's low cross at the far post to open his account in only his second appearance.
Mario Mandzukic missed the chance to make it two in stoppage time when he failed to beat Ulreich in a one-on-one situation, but the final whistle sounded shortly afterwards to ensure one goal was enough to give Wolfsburg victory.