Marc Bates’ men ended a five-meeting winless run to condemn the high-flying Rebels to their first defeat in 15 league meetings.
They were forced to dig deep in a hugely competitive encounter, but they eventually claimed a confidence-boosting win courtesy of a stunning late surge to get their season back on track.
When the sides traded blows with two 5-1s apiece in the opening four races, it became clear a tense tussle was on the cards.
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It was the visitors who took a slender lead at the halfway stage after Jason Garrity left standing at the start in heat seven, but a slice of luck ensured the Tigers quickly moved level.
Rohan Tungate hit the front in heat nine but came to a sudden halt due to a shed chain on the second lap, allowing Dimitri Berge to hit the front after avoiding a potentially nasty collision.
Rebels man Wright was not as fortunate in the next race as he was sucked into the air fence on bend two of the opening lap, and being forced to withdraw with a suspected concussion.
Simon Stead took full advantage to dive underneath Starke in the rerun and give his side a two-point lead.
Having gained the upper hand entering the closing stages, Garrity spectacularly held off the swarming Josh Grajczonek in a hammer-and-tongue heat 11 battle.
Under-fire reserve Sissis then bravely wound on the throttle to squeeze around Bradley Wilson-Dean in heat 12 – and when he repeated the trick to partner Berge in the penultimate race it sealed a sensational win.
Stead and Garrity struck a 5-1 in heat 13 to all but secure victory. The pair led the home side superbly throughout, with Stead narrowly missing out on a maximum in the final race.
The Tigers will now aim to complete a quick-fire double over Somerset as they head to the Oaktree Arena for the return fixture tonight (7.30).
SHEFFIELD 50: Simon Stead 14, Jason Garrity 9+1, Dimitri Berge 9+1, Arthur Sissis 7+2, Josh Bates 6+1, Kyle Howarth 5, Nathan Greaves 0.
SOMERSET 40: Rohan Tungate 8, Jake Allen 7+2, Bradley Wilson-Dean 7+1, Josh Grajczonek 6, Paul Starke 5, Dan Bewley 4+1, Charles Wright 3+1.