The ex-Wallaby, who passed a late fitness test on his injured knee, kicked four goals and scored the match-winning try as the Falcons ended all Welsh interest in Europe.
Edinburgh did the Dragons a favour with their surprise win over Perpignan, but Chris Anderson’s men could not help themselves thanks to an error-strewn display.
But it was the fly-half performance of the 27-year-old Wilkinson that drew the praise of Newcastle director of rugby Rob Andrew.
Wilkinson recovered from a calf injury to don for the first time this season the number 10 jersey made famous by his younger brother and produce an accomplished display.
“For Mark to step in at 10 in a game of this intensity and to play as well as he did was just outstanding,” said Andrew.
“Pace-wise, perhaps he isn’t in the same league as some of our other backs but he understands how we play and he’s got good hands and good feet.”
Burke kicked the Falcons into an early 3-0 lead, converted Colin Charvis’ 24th-minute touchdown, and made it 13-5 at half-time with a second penalty following the sin-binning of Sione Tuipulotu.
The Dragons hit back with tries from wingmen Gareth Wyatt and Kevin Morgan to cut the gap to 18-12. But Burke popped up with the all-important try on 77 minutes, dummying his way past full-back Percy Montgomery, and added the conversion to complete a 15-point haul.
: Tries: Charvis, May, Burke. Cons: Burke 2. Pens: Burke 2.
: Tries: Wyatt, Morgan, Gough. Cons: Sweeney.
: Burke, May, Tait, Noon, Stephenson, M Wilkinson, Charlton, Peel, Long, Ward, Gross, Grimes, McCarthy, Charvis, Dowson. Replacements: Taione for Stephenson (70), Grindal for Charlton (7), Isaacson for Peel (66), Sititi for Charvis (57).
: Montgomery, Wyatt, Luscombe, Tuipulotu, Morgan, Sweeney, Baber, Black, Jones, Thomas, Gough, Sidoli, Ringer, Forster, Owen. Replacements: Cooper for Baber (62), Snow for Black (62), Anthony for Thomas (49), Oakley for Forster (23).
: A Lewis (Ireland).