The 34-year-old Welshman, with 104 caps for his country, produced a perfect kicking performance, slotting five penalties and also converting two tries from Tom Varndell and one each from scrum-half Joe Simpson and replacement prop Zak Taulafo.
It provided a bonus-point winning start for Wasps' new ownership consortium who took control of the club from former owner Steve Hayes this week.
Irish replied with a try from England Under-20 winger Marland Yarde and three penalties from fly-half Steven Shingler.
But they suffered their third successive defeat of the new campaign, in which they have now conceded 123 points.
Jones, replacing fellow-Welshman Nick Robinson after missing the first two matches with a back spasm, opened his Wasps account with a fifth-minute penalty.
Irish suffered another blow when prop Leo Halavatau limped off in the 10th minute to be replaced by John Ryan, on loan from Munster.
Four minutes later they missed out on the opening try when flanker Ofisa Treviranus knocked on as he crashed his way over the line.
But they drew level in the 15th minute with a Shingler penalty after the Wasps scrum was penalised.
Irish grabbed the opening touchdown after 25 minutes when Yarde scored a try out of nothing.
There seemed little danger when centres Sailosi Tagicakibau and Jonathan Joseph combined to supply Yarde, but the winger showed the ball, jinked and produced a burst of sheer pace which left four defenders standing before he crossed in the corner.
With Shingler off the pitch receiving treatment for a blood injury, full-back Tom Homer took over the kicking duties but missed the conversion.
Wasps were denied a try in the 28th minute when they were brought back for an earlier forward pass after full-back Hugh Southwell sent Varndell racing over in the left corner.
Handling errors let the home side down as they tried to over-elaborate but they forced two penalties, both landed by Jones - the second from just inside the Irish half - to go 9-8 ahead.
Shingler restored the Irish lead with a superbly-struck last kick of the first half after the Wasps scrum were penalised a metre inside their own half.
Taulafo replaced Fabio Staibano at half-time.
The second half was only a minute old when Jones kicked his fourth penalty as Wasps regained the lead after Irish offended at the breakdown.
They forged further ahead when Varndell went over in the left corner for a well-worked try. Right wing Christian Wade split the Irish defence, Southwell again provided the final pass and Varndell supplied the finish.
Shingler kicked his third penalty to cut the Irish deficit to five points.
But Wasps, who introduced England back-row man James Haskell from the bench, made victory an inevitability when Simpson took the ball from the base of a ruck and darted in for their second try, converted by Jones.
The Welshman landed his fifth penalty before Wasps drove Taulafo, scorer of a hat-trick of tries for Wasps in the A team game against Irish last Monday, over in the left corner two minutes from time.
But Wasps had not finished. Simpson burst 50 metres from inside his own half before passing to Varndell who raced round behind the posts to touch down. Jones rounded off a hugely impressive debut by converting the final two tries.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.