Crowley's conversion made it 14-5 but Scotland hit back and after winger Jacob Henry failed to get his fingers to a cross-field kick from Chamberlain, they got in on the other wing when Jack Blain scored in the corner to cut the gap to 14-12.
Scotland pushed forward before the break but replacement prop Thomas Lambert knocked on and Crowley broke from inside his own 22 to score, fending off the challenge of Scotland full-back Ollie Smith, before adding the points to lead 21-12 at the break.
The latest Sean O'Brien to arrive on the scene - this one is through Blackrock College and UCD - set up winger Andrew Smith for the bonus point three minutes after the restart.
And then 6ft 9in lock Tom Ahern from Waterford showed remarkable pace down the right wing to finish a turnover from deep by stretching to score in the right corner and make it 33-12.
But Scotland, who finished with 14 men when replacement winger Rufus McLean was binned for a clumsy challenge on Irish full-back Oran McNulty, didn't give up.
Out-half Chamberlain scored with a dummy which will make for unpleasant viewing in the Irish video review, and while replacement hooker John McKee hit back with their sixth try six minutes from the end, Scotland secured a bonus point in the final play when replacement centre Cameron Scott got through to score.
Scorers - Ireland: J Crowley 2 tries, T Clarkson, A Smith, T Ahern, J McKee try each; Crowley 4 cons. Scotland: E Ashman, N Chamberlain, J Blain, C Scott try each; Chamberlain 3 cons
Ireland - O McNulty (Connacht); E McIlroy (Ulster), D Kelly (IQ Rugby), H Hyde (Ulster) (L Faria (Leinster) 52), A Smith (Leinster); J Crowley (Munster) (T Corkery (Leinster) 71), L Finlay (Ulster) (B Murphy (Leinster) 77); C Ward (Leinster) (C Ryan (Munster) 58), T Stewart (Ulster) (J McKee (Leinster 58), T Clarkson (Leinster) (R McMahon (Leinster 75); B Deeny (Leinster), T Ahern (Munster) (J McCarthy (Leinster) 65); S O'Brien (Leinster) (A Soroka (Leinster) 71), M Hernan (Leinster), D McCann (Ulster).
Scotland - M Currie; O Smith, J Henry, R McCallum (C Scott 77), J Blain (R McLean 46); N Chamberlain, R Frostwick (K McGhie 60); A Maxwell (T Lambert 45), E Ashman (R Jackson 35-50, 77), M Wilson (G Breese 66); K Watt (J Campbell 71), C Henderson (G Brown 71); C Boyle, J Hill, R Darge.