Ireland got their bid to become the first country to win the title outright for three successive years off to the perfect start, taking a 13-0 lead thanks to a Conor Murray try and Sexton's flawless kicking.
Wales hit back, however, with Toby Faletau bursting over the line just before halftime and Rhys Priestland coolly kicking them level just after.
It took almost half an hour for Wales's replacement flyhalf to edge them ahead, before Sexton replied with a long-range effort that sneaked over to share the points.
With trips to France and England next up, injury-hit Ireland needed to get their defence off to a positive start but neither side were happy with a draw in a championship that is more often than not decided by fine margins.
"It's a difficult one, nobody's overly happy with a draw. It's disappointing we let Wales back into it," Ireland captain Rory Best said in a pitchside interview.
In a blistering opening, Ireland put the ball through 17 phases, including some big carries from debutant CJ Stander, to threaten the Welsh line before handing Sexton two penalty opportunities to put the hosts 6-0 in front.
A limping Dan Biggar missed the opportunity to cut the deficit before departing on 20 minutes as Ireland played with the kind of intensity and stifling defence that has become a hallmark of Joe Schmidt's two-and-half years in charge.
Wales appeared rattled and scrumhalf Murray darted in for the game's first try after 27 minutes, with Sexton adding the conversion.
The momentum, however, then shifted in a breathless first half.
A Priestland penalty got Wales on the board and then the Welsh scrum tested an Irish pack containing just three of the starters that won a second successive championship in Edinburgh 11 months ago, allowing Faletau to burst over.
Wales, seeking to wrestle the title back after winning back-to-back championships in 2012 and 2013, drew level with another Priestland penalty just after the break and it took almost half an hour for him to edge them ahead.
As the rain fell, handling errors crept in and bodies tired.
Ireland eventually relented, handing Wales the lead for the first time before Sexton replied immediately as his long-range effort sneaked over to share the points.
"We managed to hang in there and we're pleased that we came back from 13 points down but a draw is not a good result for either team really," Wales captain Sam Warburton said.
(Reporting by Padraic Halpin, editing by Alan Baldwin/Toby Davis)
