A victory is a victory and was the minimum United required to edge ahead of the Gunners, but only because of the number of goals they have scored - 78 compared to 58. In a match they dominated, they would have hoped to have come away with something more tangible.
Alex Ferguson has said the championship will go down to the wire and if United beat Blackburn and Tottenham and Arsenal defeat Leeds and Aston Villa the difference will be the margin of those victories. The last time the title was this close was when the Gunners pipped Liverpool with almost the last kick of the season 10 years ago.
Maybe the tension is getting to Ferguson because yesterday the United manager was saying nothing and it was left to his assistant, Steve McClaren, to voice the visitors' thoughts. "We came to do two things," he said. "The first was to win which we did. Job done. We're pleased to be top of the League if a little disappointed we didn't put away the chances we created. Hopefully, the goals will come on Wednesday and Sunday."
Middlesbrough No2 Viv Anderson was pleased with the way the youngsters in his side competed. "I've said all along the three away games at this stage of the season are going to be a real tester for United," he said. "It's going to go right down to the wire but I wouldn't like to say which way."
On the minus side, Roy Keane had to leave the pitch after 24 minutes with an ankle injury and left Teesside on crutches. "It's a worry because he came off so soon," McClaren said. "We won't know the full extent of the injury until after 24 hours."
The Riverside has many splendid qualities, but the cauldron of hate it is not and after the vitriol among the draws of Elland Road and Anfield the United players must have thought they were hearing things when their names were read out without the customary boos.
The reception on the pitch was certainly hot, however, and Mark Summerbell's first meaningful contribution was to catch Keane from behind, a blow which would cause the United captain to limp and eventually retire from the field.
Three minutes later Summerbell's boot contributed in a more creative manner when he swivelled from Brain Deane's knockdown and flicked the outside of a post. Deane also had a chance when Dean Gordon's shot was so mis-hit it became a pass. The Boro striker was clear, but in his haste to turn he lost his bearings and his attempt was pulled wide.
These flurries in the visiting area were the exception because United controlled proceedings, building patiently - too patiently at times for their supporters - and picking at the Boro defence to find their weakness.
It soon became apparent it was an offside trap that was as deadly for the perpetrators as it was for the intended victims. After 14 minutes Jesper Blomqvist teed up Keane whose shot smouldered too fiercely for Mark Schwarzer and as he dropped it Teddy Sheringham reacted first to tap in the rebound.
The linesman halted United's celebrations by waving for offside, a decision that was proved to be wrong by the television replays, but if that was controversial it was overshadowed by the goal that arrived seconds before the interval.
David Beckham arced over a free-kick that was cleared only for Nicky Butt to loop a pass back into the Boro area. Was this offside? Sheringham, who made the first header, certainly was not but when Butt made the pass Yorke was retreating from an illegal position and it was a question of whether he was interfering with play.
He certainly was seconds later because Sheringham dinked a delightful header across the area and, as Schwarzer gave a passable impression of someone watching a tennis match, crossing his eyeline, Yorke turned to head in for his 29th goal of the season.
United's celebrations were not cut short this time and neither were Boro's protests and their captain Andy Townsend was booked for being over-critical.
That virtually ended Boro's presence as an attacking force and the question was whether United could convert their greater share of their possession into goals. The answer, possibly critically when the championship is decided, was no.
After 50 minutes Blomqvist's cross was met at the near post by Sheringham, whose flick was saved by Schwarzer but at the cost of confusion in the home defence. David May charged in and as he tried to bundle the ball in Gary Pallister hooked the ball away.
Eight minutes later Schwarzer saved splendidly from Gary Neville after the England full-back had been put clear by Beckham's pass and after 74 minutes Yorke was denied only by a flying save by the Boro goalkeeper.
United's best chance to stretch their lead arrived with 10 minutes remaining. Beckham flicked a delightful pass through the centre of the Boro defence and Andy Cole calmly waited for Schwarzer to commit himself before lobbing over him. A goal seemed certain but the ball bounced on top of the bar and away. Championships are won and lost on such fractions.
"We're counting down," McClaren went on, "and there's four games to go. Our belief is that with the way we're playing and the talent the players have we're capable of winning all four."
Unfortunately for United, in the Premiership at least, wins may not be enough.
Goal: Yorke (45) 1-0.
Middlesbrough (3-5-2): Schwarzer; Vickers, Gavin (Campbell, 71), Pallister; Stockdale, Mustoe, Summerbell, Townsend, Gordon; Deane, Ricard. Substitutes not used: Maddison, Armstrong, Baker, Beresford (gk).
Manchester United (4-4-2): Schmeichel; G Neville, May, Stam, Irwin; Beckham, Keane (Butt, 24), Scholes (P Neville, 90), Blomqvist (Cole, 65); Sheringham, Yorke. Substitutes not used: Brown, Van der Gouw (gk).
Referee: G Barber (Pyford).
Bookings: Middlesbrough: Townsend, Campbell. United: G Neville, Beckham, Sheringham, Scholes.
Man of the match: Stam.