Scotland struck back almost immediately, 19 phases of play ending with Blair Kinghorn finding Darcy Graham on the wing and he went over in the right-hand corner.
Finn Russell converted to reach the 300-point mark in the Six Nations.
There had been serious questions posed about Crowley’s kicking – both at the posts and line kicking – but he pinged a penalty to touch within metres of the Scottish line.
From the resulting lineout Dan Sheehan, fresh from sitting out the Wales game, went over. Crowley converted for 14-7.
Robert Baloucoune is known as ‘The Cat’ and the Ulster wing showed some deft footwork to score Ireland’s third try, after a terrific long pass by Stuart McCloskey.
Baloucoune, one of the stars of the tournament, managed to ground the ball before his feet went into touch.
Crowley’s conversion was wide but the hosts were 19-7 up and one try away from a bonus point before the 20-minute mark.
Scotland twice went into the Irish 22m area and both times the hosts turned the ball over – Tom O’Toole doing brilliantly to rob Kinghorn of the ball – and on a third occasion the Irish won a penalty.
The Scottish backline was also not the smooth operating machine it had been against the French and Sione Tuipulotu’s knock-on right on halftime summed up a misfiring first period.
The second half began at the same frenetic pace.
The Scots laid siege on the Irish line, the home side finally cracking as Russell sliced through for his 11th try for his country. Russell converted for 19-14.
Back came the Irish and over went Darragh Murray, just minutes after coming on for his Six Nations debut, which was converted by Crowley for 26-14.
The Scots, however, just would not let the hosts ease up, storming back with Rory Darge charging over. Russell converted to make it a five-point game again.
Farrell threw on several pairs of fresh legs with 15 minutes remaining, including Bundee Aki returning after missing the first three matches because he was suspended.
Aki made his mark immediately playing a key role in a superb move which climaxed with O’Brien going over. Crowley converted for 33-21 with 12 minutes remaining.
Crowley had been excellent in defence and offence, and took a brilliant contested catch which had Farrell on his feet.
He then slotted over a penalty for 36-21.
The Scots pressed hard but the Irish defence held magnificently and forced the visitors into an infringement on their line with minutes remaining.
There was still time for the Irish to cap a fine display as another loose Russell pass ended with O’Brien showing his searing pace to go over for his eighth try in nine Tests.
Crowley – with the Fields of Athenry ringing round the ground – converted superbly and ran to embrace his teammates.
