It sparked Stoke into life, and seconds later Edwin van der Sar was forced to dive away to his left to save a long-range effort from Fuller.
United were then troubled by a typical long throw from Rory Delap, but Danny Pugh headed over from eight yards.
Ferguson knew how important three points would be, and he made a positive change by sending on Dimitar Berbatov for John O'Shea.
Stoke, having finally built up some momentum, were reduced to 10 men with 20 minutes left when Wilkinson, having already been booked, stupidly clattered into the back of Ronaldo and was deservedly sent off.
Neville hails 'massive' Man Utd win
There was no excuse for the challenge, although Ronaldo was also fortunate to escape with a kick at the Stoke defender a few minutes earlier.
Rooney had also shown signs of indiscipline earlier by throwing out an elbow at Abdoulaye Faye in a touchline clash.
Stoke were firmly on the back foot after the sending off, with Berbatov heading over and Sorensen saving from Rooney's rising drive.
And United broke the deadlock with seven minutes left as Tevez thrashed home a finish from six yards after Berbatov turned on Neville's cross.
Ronaldo almost made the victory more emphatic with a free-kick that flashed inches wide - but Stoke were unable to mount a late surge and United claimed a crucial three points.
Stoke City manager Tony Pulis: "Andy's a smashing lad and he's had a great game but the second challenge was a poor challenge, he's given the referee no option.
"Having said that, I thought his first booking was a poor decision by the ref. But the second one, you have to be thinking as well as playing.
"We were very much in the ascendancy before the sending-off. We're very disappointed we've come away with nothing."
Manchester United manager Sir Alex Ferguson: "Hopefully we will look back and say this was a significant win for us.
"If we get to New Year's Day and are only a point or two away, then we will have a chance.
"Stoke are very resilient, determined and gutsy. However there is no question it was a sending off as it was a rash challenge by their player."
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