The Dragons, who are yet to win away from home in the RaboDirect PRO12, opened the scoring through prop Phil Price but Wasps hit back immediately with a penalty from fly-half Ryan Davis.
Jones added a penalty and a cracking drop goal to stretch the Dragons lead before John Hart's score midway through the half, and Davis' conversion reduced the lead to 11-10.
Tom Varndell put Wasps in front with a try in the corner but record-breaking youngster Hallam Amos scored on his regional debut to put the Dragons back in front at the break 21-17.
Wasps went back in front through Ross Filipo but a drop goal and penalty from Jones looked to have sealed for the Dragons.
Simpson then pounced, with Robinson converting, only for Jones to nick it for the Dragons at the death.
Meanwhile a young Ospreys side gave Northampton a scare at the Brewery Field, eventually losing 32-22 as the English side secured a bonus point LV= Cup victory.
The Saints included England quartet Ben Foden, Chris Ashton, Dylan Hartley and Courtney Lawes as well as Tongan international Soane Tonga'uiha, with hooker Hartley showing his class with two tries.
Despite their vastly more experienced opponents the Ospreys led 19-10 at the break with fly-half Matthew Morgan kicking four out of four first-half penalties and centre Sonny Parker picked off a pass from Russia wing Vasily Artemyev to score on the stroke of half-time.
Northampton's first-half points came firstly from the boot of Ryan Lamb after Ospreys captain Tom Smith was sin-binned for throwing a punch, while Artemyev crossed for the Saints with Lamb adding the extras.
The hosts' half-time lead was all the more impressive with scrum-half Tom Habberfield yellow-carded for obstruction on 35 minutes.
With the Ospreys, who currently sit top of the RaboDirect PRO12 table, still down to 14 men, the Saints pounced with a try two minutes into the second half as Hartley went over from a line-out drive.
And the power of their pack gradually wore the home side down as they scored two converted tries in as many minutes.
First Hartley crashed over for his second before flanker Clark was put over on the right-hand side courtesy of a pinpoint Lamb cross-kick.
Morgan did put over a fifth penalty on 62 minutes but the losing bonus point was taken away from the Welsh side in the final minute with a Stephen Myler penalty.
63x46.png){kind=logo}