Gibson-Park, Robert Baloucoune and replacement back Tommy O’Brien all ran in tries before the interval, with Dan Sheehan powering over from close range early in the second half for Ireland’s bonus-point score.
Discipline again proved a problem for England, with fullback Freddie Steward and No 8 Henry Pollock, making his first Test start, both shown yellow cards in skipper Maro Itoje’s 100th Red Rose appearance.
Ireland dropped Sam Prendergast from their matchday 23 entirely after the fly-half’s error-strewn display in last week’s unconvincing 20-13 win at home to Italy, with Jack Crowley installed in the No 10 shirt.
Ireland coach Andy Farrell also recalled British and Irish Lions Gibson-Park, Tadhg Beirne, Tadhg Furlong and Josh van der Flier.
Crowley opened the scoring with an eighth-minute penalty.
Committed Irish defence kept England at bay and the hosts did not help themselves when veteran first five-eighths George Ford kicked a penalty dead when trying to set up an attacking lineout.
Ireland’s defensive effort was rewarded when Gibson-Park caught England cold in the 19th minute, his quickly-taken tap penalty near the line leading to an opportunistic try.
Crowley landed the tough conversion from out on the left.
England halfback Alex Mitchell went off injured in the 25th minute.
Amid the disruption, England were 15-0 behind after Ireland scored their second try in the 28th minute.
Stuart McCloskey burst through England’s defensive line, with the 33-year-old centre sprinting clear before Gibson-Park’s cut-out pass sent in Baloucoune at the corner.
To make matters worse for England, fullback Steward was yellow-carded for an illegal challenge on Gibson-Park.
Crowley missed the conversion but England had another mountain to climb after last week falling 17-0 behind against Scotland.
Italian referee Andrea Piardi went off injured, with France’s Pierre Brousset taking his place, but there was no change to the course of the game as Ireland scored a second try in two minutes and a third in 10.
Baluconne burst through the porous cover, his simple pass sending in O’Brien for a try in front of the posts that Crowley converted.
In the last play of the half, a rare spell of sustained England handling ended with replacement Marcus Smith, on for Steward, sending in centre Fraser Dingwall for a try converted by Ford.
Ireland, however, attacked again at the start of the second half with a surge towards England’s line ending in a yellow card for Pollock.
From the ensuing close-range penalty, Sheehan powered over.
Ford sent-in recalled centre Ollie Lawrence for a 55th-minute try that the standoff converted to cut Ireland’s lead to 29-14.
But two Crowley penalties in the final quarter put the result beyond doubt before fullback Jamie Osborne dived over for Ireland’s fifth try in the 70th minute, with Gibson-Park leaving the field to huge applause from the travelling fans.
England replacement Sam Underhill scored a try four minutes from time but by then the damage had been done.