Fly-half David Humphreys, captaining his country for the fifth time, kicked 13 points to take his record points tally to 560.
Brave Romania, for all their effort, could only boast four penalty hits from recalled scrum-half Petre Mitu by the finish.
Three times their impressive pack forced television match official Derek Bevan into denying them tries in the second half, though.
Coming on the back of last week's 30-14 defeat by Australia, Eddie O'Sullivan made five changes to his side - pairing Ulster duo Humphreys and Kieran Campbell at half-back, and bringing two Bests, unrelated prop Simon and flanker Neil, as well as Leicester lock Leo Cullen into the pack.
Fittingly, Ireland, with six Ulster players included from the kick-off, wore black armbands to commemorate the passing of former Manchester United and Northern Ireland footballer George Best.
Romania - helped by a barracking breeze - were 6-3 up with 11 minutes on the clock.
Mitu slotted kicks on eight and 11 minutes to cancel out Humphreys' fifth-minute penalty success.
The Oaks' mighty pack was bossing the issue but once Ireland cut out the turnovers, the scores came.
Their first decent opportunity from a 19th-minute lineout inside the Romanian 22 was denied by number eight Ovidiu Tonita. But four minutes later, Campbell, with his right boot missing, sent Murphy sniping through the visitors' defence and Trimble popped up on his shoulder to take the pass and dot down behind the posts.
Humphreys converted and an upping of the tempo from Ireland, combined with a yellow card for Alexandru Manta for repeated offside, saw them roll up to half-time with a 17-6 lead thanks to Best's try.
Five minutes before the break, Best, from a Humphreys offload, skated inside prop Petru Balan and through the weak tackle of Gabriel Brezoianu to score by the posts.
Humphreys converted, but the Ulster veteran almost handed Romania an outlet back into the game three minutes into the second half. He was badly charged down by Ionut Tofan, but Ireland regrouped well inside their own 22 and from a subsequent Humphreys garryowen, they garnered their third try.
Full-back Catalin Fercu knocked on as he attempted to gather the kick, Trimble waded in to claim possession and neat hands from Gordon D'Arcy, Cullen and Tommy Bowe saw possession come back to the 21-year-old Trimble who gleefully charged over for his second try in just his second appearance in green.
Humphreys' conversion for 24-6 was cancelled out as Mitu landed two penalties into the wind - the first on 48 minutes being particularly impressive from 45 metres out.
Those kicks kept Romania interested and their pack, with Balan, Tonita and flanker Alexandru Manta carrying the fight, were unfortunate not to gain a try when camped three times on the Irish line.
O'Sullivan's then scored three tries in the closing 22 minutes.
First O'Connor escaped the right-wing challenge of Tonita to ghost in for his first try on 58 minutes.
Then Murphy outmuscled substitute Xabi Gal to score his 16th Test try and Dempsey, barely on the pitch, grabbed the 14th of his 62-cap career on 73 minutes to round out the win.