Thanks to Spurs' 2-1 win over Chelsea and their own last-gasp win over Manchester City last week, United are now one point behind Carlo Ancelotti's team, who host Stoke City on Sunday.
With games against Spurs, Sunderland and Stoke to come United could finish with a flourish, pouring the pressure on a Chelsea side who still have to visit Liverpool before finishing off against Wigan Athletic, who beat the Londoners at home in September.
Tottenham's dream double has put them in pole position for fourth place but the odds of them making it three memorable, and hugely important wins in a row and knocking United off course, are long.
"If we are not afraid we can win at United," said striker Roman Pavlyuchenko.
"They are a superbly-tuned machine but on our current form we should not be frightened. We have a difficult finish to the season, with two journeys to Manchester. We have a depressing recent run of results at Old Trafford and we need to correct it.
"I'm sure the Manchester City game (on May 5) will prove decisive in determining who gets fourth."
United, who would have hoped to have been in Champions League action this week but will instead turn up for Saturday's game on the back of a rare full week's rest at this stage of the season, know that this game represents their toughest remaining hurdle as they seek an unprecedented fourth successive title and a record 19th in all.
Chelsea, who have a three-better goal difference than United, must have thought the title was coming their way before last Saturday's double setback of their defeat by Spurs and Paul Scholes's stoppage time winner for United at Eastlands.
"What happened on Saturday was disappointing, especially with Manchester United's result," said midfielder Frank Lampard.
"When they scored in the last minute it was hard. If they had drawn the game it would have left us in a very healthy position but now it's tighter."
