After starting last month 18 points behind championship favourites Chelsea, Ferguson's men will close the gap to just four if they condemn the Black Cats to a defeat at Old Trafford tonight, which would confirm their relegation back to the Football League.
And Ferguson feels such a position would pile the pressure on Chelsea ahead of their hazardous trip to the Reebok Stadium tomorrow.
The United boss has not forgotten it was Allardyce's team which inflicted the damage on Arsenal three years ago by taking two valuable points off the Gunners, which opened the door for the Red Devils to steal the title back.
And he is convinced Bolton can do the same to a Chelsea side - which has won just one out of their last seven away games in all competitions - and blow the title race wide open.
Ferguson said: "Bolton did us a favour in 2003 and hopefully they will do us another. The Reebok Stadium is not the easiest place to go - we were the first team to score two goals there this season and had to play very well to get that result.
"Sam has a group of honest players there and I am really hopeful they will do us a turn. If they could get a draw, or even win, it would be a massive turnaround in the championship race."
A run of nine successive United victories has created intrigue in a title race which Chelsea appeared to have rendered non-existent by Christmas. The manner of the 10-man Blues' comeback win over West Ham last Sunday does not suggest they are feeling undue pressure at United's surge.
But, from experience, Ferguson knows Chelsea will be looking fearfully over their shoulder, particularly as the Red Devils still have to visit Stamford Bridge.
Significantly, the cup commitments of Chelsea and Middlesbrough mean the potentially-crucial encounter between the top two is now the third last game for both clubs, rather than the second last.
And, while it is a mighty ask against a side who have dropped only two points on home soil all season, a United victory on April 29 would really leave Chelsea quaking.
"Chelsea know we are there. There is no disputing that fact," said Ferguson, whose side's final two games, both at home, against Boro and Charlton, are somewhat less arduous than Chelsea's May 2 trip to Blackburn or last-day encounter with Newcastle when Alan Shearer makes a final competitive appearance at St James' Park.
"I still feel the league decider will be at Stamford Bridge. We know if Chelsea win or draw that game it is over but we have to go to Stamford Bridge and prove ourselves," said Ferguson.
"Who knows what stage the league will be at by the final week but it is pretty exciting just now."
Key to everything though, will not only be gaining maximum points against Sunderland, but also making deep inroads into Chelsea's eight-goal advantage in the goal difference stakes.
The Black Cats have not won at Old Trafford since 1968 and rarely in the intervening years can they have travelled over the Pennines with the odds so stacked against them.
In theory, the only thing which can prevent a United victory are the hosts themselves, although Ferguson has detected no hint of complacency from a side expected to see the return of Wes Brown to the starting line-up and Gabriel Heinze to the bench.
"I don't anticipate any complacency because the form of the team is excellent. The area we have to pay attention to now is the goal difference because that could be important.
"At the moment, we are eight goals behind Chelsea and we have to do something about it."