Corofin were forced to dig deep to overcome a dogged Tir Chonaill Gaels side at Ruislip yesterday, eventually winning by 0-9 to 0-2.
The Galway champions will need to up their game considerably when they meet Leinster kingpins St Vincent's in the semi-final in the New Year.
Corofin led by just a single point at the break after failing to utilise the strong breeze. But Gaels' hopes of a first All-Ireland quarter-final victory in 15 attempts were dashed after the restart as half-forward Gary Sice kicked five points.
Corofin had hit 14-45 in their previous three championship games, but they struggled to break down their hosts during a scrappy first half.
Playing with a strong breeze, Corofin enjoyed lots of possession and opened the scoring after two minutes when Michael Farragher punished a defensive error.
But the visitors' next score didn't arrive until the final minute of the first half, which was due to a combination of excellent Gaels defending and some wayward shooting.
Substitute Brian Collins made a vital interception on 12 minutes but Corofin should have found the back of the net moments later when Ian Burke sent captain Michael Farragher racing through.
The half-forward went for the top corner but saw his shot go inches past the post.
Sice had another attempt blocked as Corofin continued to press, but Tir Chonaill Gaels enjoyed a dominant spell towards the end of the first half.
With Aidan Downes excelling in a sweeper role, Cathal O'Neill levelled matters on 24 minutes when he blasted over from close range.
Declan Traynor did well to catch a Sice shot before it dipped over the crossbar, but the Gaels goalkeeper was fortunate to not be punished after he embarked on a foray upfield, only to be dispossessed on halfway.
Ian Burke, who had previously been off target from a free, once again failed to hit the target. Martin Farragher ensured Corofin led at the break after he gave Philip Butler the slip and pointed.
Sice was guilty of another glaring wide during the early stages of the second half, firing wide from a close-range free, but instead of letting his head drop, the miss had the opposite effect.
Sice boomed a superb point, and he added two more from placed balls as Corofin hit four scores in eight minutes to leave their opponents chasing the game.
Tir Chonaill Gaels were gifted a glorious goal chance on 42 minutes when Thomas Healy's short kickout went straight to Darren Gilsenan, but Cathal Magee took his eye off the ball and it allowed Healy to redeem himself.
Sice added another pair of frees in the final quarter as the game began to peter out, while some late pressure from TCG was rewarded with the consolation of a late score from substitute Eoin O'Neill.