Vunipola had not featured for Sarries since October because of a broken arm, but he made an immediate impact on his first game back, scoring the game's opening try after six minutes.
After a lively break from David Strettle and Alex Lozowski, Saracens recycled the ball out to Vunipola on the left wing and he barged his way over the line despite the presence of two defenders.
However, Sale quickly got itself back into the match when Sam James and Denny Solomona exchanged passes on the left for the former to touch down.
Five-eighth Robert du Preez missed the conversion to level the scores but he made no mistake soon after as Sale took the lead thanks to Solomona's stunning score, the winger racing from the halfway line to touch down.
Penalties from Owen Farrell, who also received a yellow card for a high tackle, kept Saracens within five points, but Sale's solid defence was able to keep it ahead.
Saracens continued to push with Farrell's precise kicking getting them in good positions, only for handling errors to creep in at regular intervals to ease the pressure.
Instead it was Sale that kept the scoreboard ticking over in the second period, Du Preez twice splitting the posts from the tee.
Those kicks proved crucial as Sale hung on to complete a memorable victory after Nick Tompkins went over in the closing minutes for Saracens, which picked up a losing bonus point to take over from Exeter Chiefs at the top of the table.