England number eight Vunipola, to be questioned by the Rugby Football Union after showing support to a homophobic Instagram post published by Israel Folau, was not given a warm reception by the Ashton Gate crowd when he was introduced to the contest in the second half.
And a bad day for the visitors was capped when another replacement, fly-half Ian Madigan, kicked a penalty seconds before the final whistle to give Bristol a desperately-needed victory over their second-placed opponents.
It was close throughout, with Saracens getting tries from scrum-half Tom Whitley, centre Marcelo Bosch and replacement prop Ralph Adams Hale – all of which were converted by Alex Goode.
Bristol flankers Steve Luatua and Dan Thomas went over, with fly-half Callum Sheedy adding two penalties and two conversions before Madigan's kick.
Saracens, who left their big guns on the bench ahead of their Heineken Champions Cup quarter-final against Munster next weekend, were on the board after six minutes.
Fly-half Max Malins ran down the wing to near the 22 and threw an inside pass to bisect the home defence and give Whitley, on his first Premiership start for the visitors, an easy run-in.
Sheedy immediately hit back with three points from a 26-metre penalty and Bristol put Saracens under the cosh, coming close to a try from an attacking line-out but knocking the ball on and giving their opponents the chance to clear.
It was, though, a half of rugby where the kicking game from both sides was off kilter. The swirling wind and cold conditions did not help, while further Bristol attacking territory was wasted by errors just metres from the line.
Sheedy had long-range kicks before the break, missing one but booting the second to put his side a point behind their high-flying opponents.
And a super move, with scrum-half Andy Uren breaking from halfway, passing to wing Alapati Leiua and then giving a sweet pass inside, put co-captain Luatua over. The touchdown as converted by Sheedy and Bristol were six points up.
Sarries boss Mark McCall brought on Vunipola after 51 minutes and soon after Bosch drover over, after home hooker Harry Thacker was sin-binned for illegality at a try-line ruck. Goode added the extras.
Back came the home side and, when prop John Afoa ran like a centre through a gap in midfield, he was able to feed Thomas for a try under the posts.
However, Saracens thought their day was done when Bosch was driven over the line, with Goode's conversion putting them a point in front.
But Saracens infringed 30 metres from their line with 11 seconds to go and replacement Madigan calmly landed the kick for a dramatic victory.