Feyenoord were already two goals down when Zlatan Ibrahimovic's pull back from the byline was diverted into the net by Jones's heel.
Wayne Rooney had earlier become United's all-time leading scorer in Europe as Jose Mourinho's side eased to victory.
Twelve years after starting his continental tally with a hat-trick on debut and five days after vowing he was 'not finished yet' as an England international, Rooney moved beyond Ruud van Nistelrooy's haul of 38, and one behind Sir Bobby Charlton's all-time tally of 249, with a cool first-half dink.
It was then Rooney's brilliant reverse pass that allowed Juan Mata to double the lead in the second half before an own goal from Jones and a Jesse Lingard strike made it 4-0, ensuring United need just a point against Zorya Luhansk in two weeks to progress.
There were other positives for Mourinho to take - not least Henrikh Mkhitaryan's impressive outing on his first start in two months - but this was a night that belonged to Rooney.
Fenerbahce's victory over Zorya earlier had left Mourinho's side with a simple equation - lose and they were out or secure four points in the final two games and they would advance.
Mkhitaryan's involvement, which had been promised by his boss, saw him largely occupying the left flank under Mourinho's glare, and he looked keen to impress with several nice touches most obviously demonstrated with four first-time passes exchanged with Rooney which nearly produced a chance.
Opportunities did fall to Paul Pogba, whose attempt was pushed over by Jones, and Michael Carrick when his measured effort from the edge of the box was diverted away by a combination of ex-Liverpool duo Jones and Dirk Kuyt.
The latter had been afforded a reception typically reserved for those to have called Merseyside home, though he almost silenced the Old Trafford faithful with an effort Sergio Romero diverted past his post with a flick of his right foot after the keeper had also saved from Rick Karsdorp.
Kuyt was operating in a central-midfield berth, one some have suggested may suit Rooney more, but he showed his value further forward with the opener.
The 31-year-old instigated the move by breaking down the left and feeding Ibrahimovic inside on a three-on-four break which evened up when Rooney's marker Jens Toornstra lost his footing, allowing United's captain to collect a return pass and deliciously lift the ball over the onrushing Jones.
The desire to formulate the attack and the poise to round it off was reminiscent of Rooney's earlier days in red, though back then the pacy teenager may have reached Pogba's second-half chipped pass over the top which, on this occasion, bounced away into Jones's arms.
A side Mourinho had dubbed 'the unlucky team in the Premier League' at the weekend seemed intent on wrapping up matters after the interval, with Mata's own chipped effort from range brilliantly tipped over by Jones.
Mata turned the ball home minutes later but even the most fortunate club in the land would have seen the offside flag raised given how far Mata had strayed beyond the line.
Of United's attacking outlets it was Mkhitaryan, with his purposeful runs and excellent close control, who was impressing the most and he fired into the side-netting after a give-and-go with Ibrahimovic.
Any fears United would fail to make their dominance count were dispelled with two goals inside six minutes.
The first, in the 69th, came after Carrick won the ball back, Ibrahimovic flicked through to Rooney in the box and he displayed the vision to find Mata inside to leave him with a routine finish.
It was Mata's last act, though not United's, and for once luck was on their side as Jones put the ball into his own net.
Rooney and Mkhitaryan made way to gratuitous applause with the job done and further gloss was applied by one of their replacements as Lingard finished from the edge of the box in stoppage-time.
