A moment of individual brilliance from Charlie Shiel helped give Edinburgh a fighting chance of making the play-offs in the United Rugby Championship. The replacement scrum-half ran in the winning try from deep in his own half as the visitors beat Connacht 31-21 in Galway. Edinburgh remain outside the top eight with one round of fixtures remaining but the bonus-point victory at the Dexcom Stadium means Sean Everitt’s side can go into their final league match - at home to Ulster on Friday - knowing another five-point win could open the door to the play-offs for them for the first time in three years. With play-offs rivals Munster and Benetton due to play each other, Edinburgh can benefit regardless of the result in Cork. Connacht knew before kick-off that their hopes of making the top eight had gone and the Lions, Ulster and the Ospreys also dropped out of the reckoning on what has been a pivotal weekend. “It's all in our hands now," said Everitt. “This is a fantastic win away from home because this is not an easy place to come to. Charlie provided that special moment, which was great for us. But it wasn't a one-man effort, it was a squad of 23 that won the game. “The guys will be happy tonight, but it's a short turnaround and a massive game against Ulster next week. Another five points is a must for us.” Pierre Schoeman got the ball rolling for the visitors, crashing over after Ali Price had teed him up as Edinburgh capitalised on a string of lineout infringements by Connacht. Thompson converted and it was the perfect start. But Connacht hit back and captain Cian Prendergast crossed for a try only for referee Ben Breakspear to chalk it off after a replay showed No 8 Sean Jansen in an offside position obstructing an Edinburgh defender. Edinburgh made the most of the let off and scored a brilliant try through Hamish Watson. The backs worked it out wide, with particular kudos to Jack Brown for his delayed pass. Watson, flying down the left wing, still had plenty to do but had too much pace for Connacht and dummied Santiago Cordero before scoring in the corner. It was splendid stuff and Thompson added the extras to make it 14-0. Edinburgh’s lead was halved at the start of the second half as winger Finn Treacy finished off a slick move and Hanrahan landed the conversion. There had been a distinct shift in momentum and Connacht soon drew level. It was Treacy again who did the damage, taking a no-look pass from scrum-half Ben Murphy to score his second. Hanrahan converted. Worse was to follow for Edinburgh as they lost Mosese Tuipulotu to injury. The centre had been tackled by the combined efforts of Hanrahan and Bundee Aki and Breakspear had a look at it before deciding there was no foul play. Tuipulotu had treatment on his knee and was clearly in a lot of pain as he was wheeled off on a stretcher. He was replaced by academy player Findlay Thomson, a late replacement on the bench for James Lang. Edinburgh needed to wrest back control and Muncaster restored their lead at the halfway point of the second half. Marshall Sykes won a lineout and although the maul was a little messy, Ewan Ashman got to within a yard of the line before Muncaster bulldozed his way over. Thompson’s conversion made it 21-14 but Edinburgh’s lead lasted only five minutes. Cordero found Shayne Bolton with a looped pass and the Connacht winger scored in the corner. It was a tough conversion but Hanrahan landed it to tie things up at 21-21. It was turning into a real nailbiter and Shiel produced his special moment with less than seven minutes left. The replacement scrum-half shaped to box kick at the base of a ruck then sped off from deep in his own half. Connacht were slow to react and Shiel slalomed his way past the green jerseys to run in a brilliant individual try. Ben Healy, on for Thompson, converted, then added a late penalty to make it 31-21 to Edinburgh.