Sexton initially took a whack to his left eye in the 19th minute when Jonathan Davies' knee landed in his face.
North's second try of the evening early in the second period put the Dragons on their way to a first win in three, which Halfpenny added to with the extras from close to the touchline.
Wales sowed up the victory in the 78th minute when Roberts touched down after a brilliant block down of Sexton's kick.
Wales - reeling from successive defeats - started with real goal but Ireland matched their efforts with frenzied defending.
Wales drove the line-out towards the line but Ireland held-firm.
They seemed to sense that Ireland might lack the organisation which normally follows from Sexton's presence on the pitch. At the front end of the champions it was our defence, now it is our attack.
The scrum-half fed the ball wide and North barrelled through Simon Zebo and Keith Earls from 15 metres out to score.
Ireland looked to have survived without incident until Webb found Liam Williams with a cross-kick. Sexton made six tackles in that opening quarter alone.
Wales thundered back into the contest early in the second half and got over the Irish line to level matters.
Wales enjoyed a superb defensive display and led 8-6 at half-time thanks to a 20th minute try from North, who bulldozed his way past three men and over the line, and a Leigh Halfpenny penalty.
George North led the resurgent Wales performance with a pair of tries as Ireland struggled to cope with his power and pace. He hurt it again moments later but again continued.
The Munster man was visibly carrying his left arm and it seriously limited his ability to both tackle and pass.
It didn't last long however, as the free-scoring Welsh rediscovered the form that saw them score 65 points in Scotland last time out.
It could have been worse for Ireland had Dan Biggar been successful with a drop-goal attempt. Wales out-half Ben Jones switched the play to the open side and put Corey Tarrant through a gaping hole to score.
An energy-sapping 26 phases of play brought no reward but soon afterwards Sexton converted an easy penalty to leave Ireland within a converted try.
For all their fervour and sense of goal in front of their own supporters, they would have been staring at defeat but for a moment of stupidity from Ireland's centre Robbie Henshaw who, 11 minutes from time with his side trailing 15-9, joined from the side a maul that was heading for the home line without him and turned a certain try for Ireland into a penalty for Wales.