Roberto Mancini's men travel to Tyneside level on points with the Red Devils but with a vastly superior goal difference, meaning two victories should see them win the Premier League title.
Although they will be pitched as underdogs against City, Alan Pardew’s side beat Chelsea 2-0 on their own turf last time out thanks to two magnificent Papiss Cisse goals.
They also beat Sir Alex Ferguson's side 3-0 in January and Jones hopes the Magpies are capable of a similar performance this weekend.
“They were terrific that night,” said Jones. “They pressed us really well and we didn't get going.
“But I have said all along, Newcastle are a terrific team with some fantastic individuals. Cisse's two goals the other night were incredible, so let's hope they can do us a favour.”
United failed to muster a single shot on target in their visit to the Etihad Stadium on Monday as City ran out 1-0 victors courtesy of Vincent Kompany’s headed goal.
“There have obviously been a lot of questions raised and rightly so,” Jones said.
“We didn't play to our best on Monday, which was disappointing. But make no mistake about it, we are still there.
“We are on level points with them. Only goal difference separates us at the moment and we have seen already this season there have been so many twists and turns.
“Don't be surprised if you see a few more.”
Jones admitted the squad were low in the immediate aftermath of Manchester City’s triumph but insisted the players have not dwelled on the defeat.
“The disappointment turned to positivity very quickly,” he added.
“Obviously on Tuesday the lads were gutted and massively disappointed. But we have moved on quickly, pushed it to one side and put it right in training. There are still a lot of bubbly characters about.
“There is no point dwelling on it. It has happened. It has gone. We move on from it and are looking forward to the game at the weekend.”
The 20-year-old is also adamant that players’ minds will be on matters at Old Trafford despite the Newcastle-Man City match preceding United's clash with Swansea.
He continued: “We have to concentrate on what we can do.
“We have to win the two games, take six points and see where that takes us.
“I am sure what is happening at Newcastle will be in the back of everyone's minds but there is no point sitting there watching their game.
“I don't think it will be on in the dressing room because we have to prepare properly.”
The former Blackburn man went on to dismiss City boss Mancini’s claims that United have an easier final two games - at home to Swansea this Sunday and at Sunderland on May 13.
“I don't know about it being easy,” he added. “If he [Mancini] looks at the games, none of them are easy in the Premier League.
“We have seen that so often this season. There have been so many surprises and Swansea are one of them.”