Chelsea’s grit and determination are keeping them in the title race, but Sir Alex Ferguson has little to worry about as he heads to the Eternal City. The Manchester United manager need not waste any of his prayers on domestic matters and can devote all his attention to his side’s Champions League quarter-final against AS Roma tomorrow.

With a five-point lead and only six matches left, the title is United’s to lose, with Chelsea showing little sign of prising the trophy from their grasp. Avram Grant’s team will have to raise their game to previously unattained levels if they are to be victorious in the must-win home match against United on April 26, while a repeat of this poor performance could lead to defeat in any of their other five games.

Their first-team coach would not admit as much, but Chelsea need to win all of their matches to have any hope of winning the title. Having inherited a troubled team in fifth place, Grant deserves considerable credit for keeping them in contention for this long, but the feeling is reminiscent of last season, when Chelsea huffed and puffed to stay involved before running out of steam at the last as United’s superior class told.

With better finishing from Middlesbrough, Chelsea’s hopes could have been all but extinguished as, after a stupefying first 70 minutes, the visiting team roused themselves to strike the woodwork three times in nine minutes.

Afonso Alves was the most culpable, flashing a header wide, hitting a post with the goal at his mercy and then heading against the bar – efforts that made Gareth Southgate’s claim that it was the Brazilian’s sharpest performance since his £12 million arrival from Heerenveen all the more worrying.

Southgate continues to impress as an enterprising young manager and it is reasonable to assume that his game plan did not involve conceding an early goal, which at Stamford Bridge is the footballing equivalent of attempting to climb Mount Everest in flip-flops. As the match programme took great delight in celebrating, Chelsea have not lost a league match at home for more than four years, so giving them a head start is not advisable.

As a former central defender, Southgate will have been all the more frustrated that the only goal of the game, if not quite soft, was avoidable. Gary O’Neil’s foul on Michael Ballack by the left-hand corner of the penalty area presented Wayne Bridge with an opportunity to demonstrate his dead-ball skills and with him enjoying a rare Premier League outing while Ashley Cole rests for the Champions League quarter-final, first leg against Fenerbahçe on Wednesday, the England defender duly obliged.

Bridge’s free kick eluded all Middlesbrough’s defenders, with Ricardo Carvalho arriving at the far post to head home his first goal of the season.

Grant took a significant stride forward with his first victory against a top-four rival by beating Arsenal the previous weekend, but this could easily have been two steps back as Chelsea struggled against a team with little to play for.

Mark Schwarzer’s only involvement after Carvalho’s goal had been blocking speculative, long-range shots from John Obi Mikel and Michael Essien until he tipped Salomon Kalou’s header over the bar 70 minutes later, although Shaun Wright-Phillips did provide a perfect illustration of why he has been dropped from the England squad after his introduction as a substitute, with two bad misses.

The tone of the afternoon was set by television pictures of a Chelsea fan asleep on her neighbour’s shoulder, but the home team’s supporters were jolted out of their lethargy in the final quarter. Middlesbrough’s revival was sparked by David Wheater, whose long pass from his own half was missed by the onrushing Carlo Cudicini, giving Alves the chance to score an open goal, but he missed.

If Chelsea were worried at that stage, they were panicking a few minutes later when Adam Johnson delivered a free kick into the penalty area, from which first Alves and then Wheater hit the bar, while the substitute could have won a penalty when his cross appeared to roll down the arm of Juliano Belletti. Grant conceded that Chelsea were fortunate to stay in contention, but to judge from the attendance of 39,993 – Chelsea’s second lowest of the season – some fans are losing the faith.

How they rated

Chelsea (4-3-3): C Cudicini 5 J Belletti Y 5 R Carvalho 6 J Terry 5 W Bridge 6 M Essien 6 J O Mikel 5 M Ballack 5 J Cole 6 D Drogba 6 S Kalou 5 Substitutes: S Wright-Phillips 4 (for Ballack, 65min), N Anelka (for Kalou, 78), Alex (for Drogba, 90). Not used: Hilário, A Shevchenko. Next: Man City (a).

Middlesbrough (4-4-2): M Schwarzer 6 L Young 5 D Wheater 6 E Pogatetz 5 A Taylor 5 G O’Neil 5 L Cattermole Y 5 G Boateng 5 S Downing 6 J Aliadière 5 Tuncay Sanli 4 Substitutes: A Alves 5 (for Tuncay, 65min), A Johnson (for O’Neil, 80), M Shawky (for Cattermole, 90). Not used: R Turnbull, T McMahon. Next: Man United (h).