Samir Muratovic scored the second-half winner, slotting home an angled shot on a tense night which saw their nearest rivals Austria Vienna lose 4-2 at home to Salzburg after twice leading
Sturm, champions for the third time, finished with 66 points from 36 matches in the 10-team table and booked a place in next year's Champions League qualifying stage, where they will enter the fray in the second round.
Big-spending Salzburg, champions for the last two seasons, took second spot with 63 points while Austria Vienna were third with 61.
Second place will be considered slim pickings at the club sponsored by energy drinks manufacturer Red Bull.
Starting two points clear of Austria Vienna, Sturm went ahead with an Andreas Hoelzl goal in the 14th minute but Alexander Hauser headed the visitors level 15 minutes later.
Austria Vienna led twice as Roland Linz put them ahead in the 32nd minute, the league top scorer notching his 21st goal of the season, only for Jakob Jantscher to level a minute later.
The hosts regained the lead with a Nacer Barazite goal in the 73rd minute and this time were pegged back three minutes later when Brazilian Alan levelled the scores.
Roman Wallner and Alan, with his second, added two more in the next seven minutes as Austria faltered.
Sturm, cup winners last season, enjoyed a golden period during the late 1990s when they won the league twice and cup three times, including two doubles. They also took part in the Champions League group stages three times.
