Josh Manz crossed the line two minutes from time for Leicester before Orlando Bailey converted from the touchline to clinch victory at the StoneX Stadium.
Earlier on, Alex Lozowski’s opener put Sarries in control after 10 minutes when he collected Louie Johnston’s searching kick and surge over the line before Johnston converted.
Tommy Reffell responded almost immediately for the Tigers, breaking away from the maul to score and Bailey converted to level.
But celebrations were short lived as Tayo Adegbemile bulldozed his way over to put Sarries back ahead, before Rotimi Segun added a third score.
Reffell scored his second try of the match to reduce the arrears and make it 21-12, but the conversion was missed.
Finn Theobald-Thomas cut the gap to just four points after half-time, but a number of blows were still to be traded. Ollie Allan scored before ex-Sarries man Tom Whiteley kicked Leicester into a 24-21 lead.
Segun’s second put Sarries ahead but the final twist came when crossed following a maul to secure a dramatic win at the death.
Bath sealed their win over Bristol Bears thanks to three second half tries from Charlie Griffin and Arthur Green.
Bristol saw three tries, from Max Pepper, Gabriel Ibitoye and Harry Rendell all converted by Sam Worseley, who also added a penalty.
But it wasn’t enough to contain the hosts, who stepped up having trailed 17-14 at the break.
