After a woeful start to the new campaign, when they won just three of their opening eight games and found themselves in the bottom half of the Barclays Premier League, United have shoved themselves firmly back into contention.
Sunday's 1-0 win over Arsenal means they are just five points adrift of the table-topping Gunners and within striking distance of Liverpool and Chelsea, while also leapfrogging big-spending rivals Manchester City.
The latter event is particularly significant because City manager Manuel Pellegrini has been given a relatively easy time following his arrival as Roberto Mancini's replacement at the Etihad Stadium.
It contrasts sharply with the scrutiny David Moyes has found himself under at United, but Jones is not surprised that is the case.
"People want us to fail because we have won the league so many times," said the England international.
"Everyone hates the best clubs, it is as simple as that, and United won the league long before I was here.
"We enjoy that. We relish the test we get thrown at us every week."
It has always been the way with United, just as they have always tended to respond when their backs are against the wall, as they have been so far this season.
"It proves when people doubt us we are more than capable of standing up for ourselves and proving to people that is why we were champions last season," Jones said.
"We weren't champions for nothing. We thoroughly deserved all the points we got last season."
Much has been made of the fall from being champions by an impressive 11 points to potential also-rans.
After nine games unbeaten in all competitions, it seems the disparity is not quite as large as it had appeared.
For that, United do not just have Wayne Rooney and Robin van Persie to thank.
Rooney may have earned man-of-the-match honours for his efforts at Old Trafford and Van Persie might have scored the winning goal, but others deserve a mention too.
In an unaccustomed right-back role, Chris Smalling produced an admirable display, making a crucial tackle on Olivier Giroud in the final stages to deny the Gunners forward a clear shooting opportunity.
And Jones won champagne for the sponsors' best player after an outstanding effort, initially in midfield when he went on two searing bursts that unsettled the visitors' back four, then central defence following Nemanja Vidic's unscheduled exit.
"The game needed energy, especially in the middle of the park," said Jones.
"We needed to close people down and make an effort to win the ball back. We made it really difficult for Arsenal to play.
"It was a great game to be involved in. It was a fiesty affair. Tackles were flying in. The crowd were up on their feet. When you get a win like that it just makes it ever so sweet."
Jones' legacy of what first appeared to be a sickening clash of heads with Arsenal goalkeeper Wojciech Szczesny was a nasty cut above his left eye.
As it turned out, the pair got off much more lightly than Vidic, who ended up in hospital following his collision with team-mate David de Gea.
Vidic was released from hospital on Sunday night and will be monitored by United medical staff before it is decided whether he can feature in the club's next match, at Cardiff on November 24.
The news would have allowed Moyes to head into the international break in much better mood than he went into the last one.
And Sir Bobby Charlton will not be getting pestered by questions over Moyes' suitability for the job as Sir Alex Ferguson's successor.
"There was a little bit of criticism going on but I am pleased I didn't have to answer it because David has done it himself," Charlton told United Review.
"We are not the type of team who can languish in the bottom half of the league and it is promising to see us putting together some good results.
"We have had a lot of publicity from changing manager after so long and I've had the sense that teams have maybe been upping their game a little bit against us. But we have been first-class recently.
"Here we are, creeping up the table again and that is what we want."