Hamilton 1 - 4 Rangers: Pair of spot-kicks spare Rangers' blushes
Rangers had not managed to win a league match on the road since February and appeared to be in for another bout of away-day blues when Steven Boyd cancelled out Ryan Kent’s opener.
Steven Gerrard’s side were far from their slickest but got the victory which moves them up to fifth when Accies defender Alex Penny gave away two late spot-kicks.
Tavernier stepped up both times and found the net before Alfredo Morelos put a gloss on their first triumph outside of Govan since St Johnstone were beaten in Perth eight months ago.
Gerrard had used his pre-match press conference to urge his men to have the belief to kill off their away-day hoodoo after seeing them slip up against Aberdeen, Motherwell, Celtic and Livingston.
But he would have been concerned to see a pattern similar to their last trip to Livi emerge as the Light Blues struggled to find their groove, despite bossing the early possession stakes.
He could have been forgiven for suffering a sense of deja vu as Aaron McGowan and Darian MacKinnon came close to handing Hamilton an early lead.
Tavernier was then at the centre of a penalty call as Mickel Miller tumbled at his feet but referee Andrew Dallas waved play on.
Chances at the other end had been rare in the opening half hour as Hamilton showed the kind of determined focus that escaped them at Easter Road.
But all it took was one mistake four minutes before the break for those efforts to go to waste as Rangers grabbed a lead they barely deserved.
Lassana Coulibaly cut off a Ziggy Gordon pass and swiftly nudged it on to Morelos. The Colombian’s reactions were just as quick as he knocked it round the corner for Kent, who raced past Penny before clipping a fine finish over Gary Woods.
The on-loan Liverpool winger was booked for his celebrations as he dived into the away support.
However, Hamilton blew two golden chances to level as the visitors’ defence creaked again after the break. First Bingham was able to bundle through on Allan McGregor.
The Gers goalkeeper pushed away a strike that was straight at him but James Keatings had to do better than fire the rebound wide as Nikola Katic failed to sense the danger.
But Gerrard’s men were not out of the woods yet and found themselves pegged back in the 80th minute as Boyd skipped past a lazy leg from Jordan Rossiter before smashing a sensational equaliser past McGregor.
The panic only lasted three minutes, though, as two moments of madness from Penny handed Gers the win.
First the centre-back used an arm to stop a Daniel Candeias cross inside his own box before two minutes later he appeared to trip Morelos inside the area. Both times Tavernier refused to blink from 12 yards as Rangers breathed a sigh of relief.
The fight was out of Hamilton by this point and they conceded again in stoppage time as Morelos danced past Woods before clipping into an empty net.