Sane settled Bayern’s nerves after an uneasy first half, as Vincent Kompany’s side struggled once again against weaker opposition.
“It was a bit tight at the end, but we are really happy to have got the three points,” Sane told Sky.
Having dropped unexpected points against Bochum and Union Berlin in recent weeks, Bayern were under pressure to avoid a third slip after reigning champions Bayer Leverkusen narrowed the gap to three points with a 3-1 win over Bochum yesterday.
Sane insisted that pressure was a good thing for Bayern, “because it helps us keep our rhythm when we know we have to win every game”.
Yet they looked sluggish against a fearless St Pauli side who almost took the lead early on when a Jackson Irvine header hit the bar.
The visitors handed Bayern the opener on a silver platter just two minutes later, when Siebe Van der Heyden was caught napping at leftback.
Van der Heyden was robbed of possession by Jamal Musiala and Bayern swarmed into the box, allowing Harry Kane to sweep the ball in from close range.
It was Kane’s first goal against St Pauli, meaning he has now scored against every team he has faced in the Bundesliga.
Unbowed, the visitors snatched a deserved equaliser just before the half-hour mark through Elias Saad.
The Tunisian forward slipped under the radar in the Bayern box and tapped in a Manolis Saliakas cross to score his first goal since September.
Sane restored the lead after halftime, smashing the ball in unchallenged after a clever switch of play left him with acres of space on the left.
He sealed the win 20 minutes from time, turning in a Kane cross from close range after a ruthless Bayern transition.
Yet Bayern still had to survive a nervy final few minutes after Lars Ritzka pulled one back for St Pauli in added-time.
And there was more bad news for the Bavarians as defender Hiroki Ito was forced off in the final minutes, adding to a growing list of injury concerns.
Blow for Leipzig
Elsewhere, RB Leipzig suffered a blow in the race for the Champions League with a 1-0 defeat at Borussia Monchengladbach.
A poacher’s finish from Alassane Plea saw Gladbach snatch a valuable three points and leapfrog Leipzig into fifth.
Werder Bremen overtook Borussia Dortmund in mid-table thanks to a comfortable 3-0 win over bottom club Holstein Kiel.
Marvin Ducksch whipped a brilliant freekick into the top corner from a tight angle to give Bremen the lead in the first half.
Felix Agu doubled the lead after the break with an equally elegant finish, curling the ball under the bar from the edge of the penalty area, before Marco Gruell made it three in added-time.
Kiel are now five points adrift of safety after fellow strugglers Heidenheim snatched a 1-0 win away to Wolfsburg thanks to a first half penalty from Marvin Pieringer.
Augsburg’s Samuel Essende broke a Bundesliga record in his side’s 1-1 draw with Hoffenheim, scoring the fastest goal ever by a substitute.
Essende netted just 10 seconds after coming on at halftime, but Andrej Kramaric levelled from the spot later in the second half, ending a 683-minute run without conceding for Augsburg goalkeeper Finn Dahmen.