It is said to be the point at which even happy marriages can fall victim to an itch, but, as they approach the seventh anniversary of a match made in heaven, David Moyes and Everton are lusting only for silverware. That might not have appeared obvious to anyone walking past the home dressing-room at Goodison Park at half-time yesterday, but they say that the odd slanging match can do a power of good, particularly if it gets the reaction that Everton produced in the second half against Middlesbrough.

At 4.45pm, as they trudged to the tunnel 1-0 down after a wretched first half, it seemed that Everton’s opportunity was disappearing. Fifteen minutes later their players reemerged looking a different team, reinvigorated by a rollicking from Moyes and his assistant, Steve Round, and given a much-needed new dimension by the introduction of Louis Saha, who headed the second of two quickfire goals to ensure that the dressing-room to which they returned at the end of the match was a very different place.

The giddy feeling among Everton’s players might have been replaced by a slight sickness when they discovered soon afterwards that Manchester United await them in the semi-final at Wembley, but that may hold a certain appeal to some of them. Tim Howard, Phil Neville and Saha are United old boys who will relish the occasion, while Evertonians of a nostalgic bent will recall how Sir Alex Ferguson’s team were slain in the FA Cup final in 1995, the previous time that the Merseyside club enjoyed such a run in the competition.

The competition has rarely been kind to the Merseyside club in the intervening 14 years, which has witnessed humiliating defeats at the hands of Port Vale, Bradford City, Tranmere Rovers and Shrewsbury Town. Nor has the competition brought much cheer for Saha, who was overlooked for the final by Newcastle United in 1999 and missed three finals with United, cup-tied in 2004 and injured in 2005 and 2007, but he and Everton will have cause to believe that their luck is changing after he inspired the comeback that seemed unlikely when Middlesbrough took a deserved lead through David Wheater just before half-time.

It was a goal that Everton had coming to them, their first-half display characterised by errant passing and careless defending.

Middlesbrough, with Julio Arca and Tunçay Sanli running the show and Gary O’Neil and Stewart Downing showing up well on the wings, looked comfortable and could have punished Everton’s slackness long before Matthew Bates swung in a cross from the right and Wheater scored with a firm header that a nervous Howard should have kept out.

Then came what Moyes called the “talking to” and, no less significantly, the arrival of Saha. The forward was not considered fit to play for more than 30 minutes, having been troubled by a thigh injury all week, but this was an emergency. The dilemma for Moyes was which of his makeshift centre forwards to restore to midfield. He opted for Tim Cahill, who had looked ill at ease, leaving Marouane Fellaini up front.

It took just five minutes for the shake-up to pay dividends, Cahill crossing from the right and Fellaini getting between Robert Huth and Brad Jones, the goalkeeper, to send a looping header into the net. It was not Jones’s finest moment and Everton, sensing vulnerability in defence, stepped up the pressure in the following minutes. Saha, looking hungry, narrowly failed to connect with a Leon Osman cross from the right, but the ball was retrieved from the opposite touchline by Steven Pienaar, whose cross was headed in superbly by the substitute at the near post. In the space of 12 minutes the match had been turned on its head.

Middlesbrough threatened sporadically in the closing stages, with Joleon Lescott required to make a superb tackle to deny Tunçay, but they will be left to focus on the fight for survival while Everton march on to Wembley, determined to fulfil the potential that Moyes has been telling them to embrace since he arrived at Goodison Park seven years ago this week.

Everton (4-4-1-1): T Howard 4 P Jagielka 6 J Yobo 5 J Lescott 7 L Baines 7 L Osman 6 P Neville 7 J Rodwell 6 S Pienaar 6 M Fellaini 7 T Cahill 7 Substitutes: L Saha 8 (for Rodwell, 46min), D Gosling (for Pienaar 90). Not used: C Nash, L Jacobsen, S Castillo, J Wallace, A van der Meyde.

Middlesbro (4-4-2): B Jones 4 J Hoyte 4 D Wheater 6 R Huth 5 E Pogatetz 5 G O’Neil 6 M Bates 5 J Arca 6 S Downing 6 J Aliadière 5 Tunçay Sanli 7 Substitutes: M Emnes 6 (for Aliadière, 68min), A Johnson (for Bates, 72). Not used: R Turnbull, A Taylor, A McMahon, J Walker, J Franks.

Referee M Halsey Attendance 37,856