Wilson scored with a wonderful set-piece in Derby County's penalty shootout defeat of Manchester United in the EFL Cup last month, and the midfielder produced a similar moment of magic to light up a tight contest Dublin.
Buoyed by a point against Denmark in their last outing, Ireland had started well, but Cyrus Christie and Shane Duffy squandered the best of the chances Martin O'Neill's side managed to craft.
Wilson made the difference with a wicked 58th-minute free-kick, with Ireland then mustering little in response as Wales moved top of League B Group 4.
1 - Other than Gareth Bale, who had scored each of Wales' last five direct free-kicks goals in competitive matches, Harry Wilson is the first Welshman to score such a goal since Aaron Ramsey back in October 2009 against Liechtenstein. Peach. #IRLWAL pic.twitter.com/nDNOt5trUy — OptaJoe (@OptaJoe) October 16, 2018
Matthew Smith's abysmal touch allowed Christie to pounce in the ninth minute, but Wayne Hennessey made a fine save to spare the 18-year-old midfielder's blushes.
Despite Ireland's fast start, neither goalkeeper would be tested again until 10 minutes before the interval, however, when Tyler Roberts flicked a tame effort at Darren Randolph.
Ireland responded well, Duffy winning a header from Jeff Hendrick's corner, only to direct his effort straight at Hennessey.
That profligacy proved costly just before the hour, Liverpool's out-on-loan star Wilson more than filling the void left by the injured Bale by curling a delightful strike over Ireland's wall and into the top-left corner from 25 yards.
Wales could have put the game beyond all doubt 15 minutes from time – David Brooks having a close-range shot blocked before James Chester headed wide from the resulting corner.
Hennessey did have one more save to make from substitute Scott Hogan, but Wales, who missed a late chance through George Thomas, remained comfortable as they secured a back-to-back win over Ireland for the first time since March 1986.
What does it mean: Giggs' faith in youth pays off
Wales had suffered back-to-back defeats heading into Tuesday's clash, but Giggs' youthful side have certainly had the beating of Ireland over two legs, and they now sit pretty with six points heading into their decisive final match with Denmark.
Ireland, meanwhile, have just one point, and will definitely be relegated to the third tier should Denmark avoid defeat against Wales.
Wilson fills in for missing stars
Ramsey announced the birth of his twin sons just prior to kick-off, while Bale missed this batch of fixtures due to injury, but Wilson more than stepped up to the mark, and it will be hard for Giggs to drop the youngster even when Wales' star duo return.
O'Neill, Keane coming up short
The writing appears to be on the wall for Ireland's divisive duo. With both Bale and Ramsey missing, Ireland had a real chance to get off the mark, but O'Neill seems unable to get a tune out of his dysfunctional side, while Keane's fierce attitude seems to do little in terms of rallying the players either.
Both teams round off their Nations League group campaigns against Denmark, Wales hosting the Danes with first place up for grabs on November 16, before Ireland face Age Hareide's men three days later.
That game for Ireland comes after they go head-to-head with neighbours Northern Ireland in Dublin.