The wheels may have seemed at times to be rattling on their rims, the axle jangling, the spokes pinging out, but Arsenal's season-on-three-fronts continues to roll along regardless. There was even a whiff of late-season rejuvenation, springtime for Özil and Arsenal, towards the end of this 4-1 FA Cup quarter final defeat of a well-drilled and competitive Everton. By the time Olivier Giroud scored Arsenal's rollicking fourth goal with five minutes left – Tomas Rosicky and Mesut Özil, who had his best match since the start of December, creating it at the end of a sinuous move – the wider struggles of the last few weeks of winter had seemed to fade a little.

If this was a potentially season-reviving result for Arsenal, it was a bracing occasion all round for Özil, who had not scored since the last time these two teams met on 8 December and had created only one assist in his past 12 matches. Arsenal's record signing was bought to make the difference on days like these, and so he did, creating more chances than any other player, scoring one and making one, and possibly even providing a decisive full-stop on a traumatic few weeks during which being wheeled out to play football twice a week has seemed a peculiar kind public trauma.

"He looked physically regenerated," Arsène Wenger said of the German afterwards and Arsenal's manager also looked encouragingly perky here. For all their early-season progress Arsenal have been in a state of mild disintegration these last few weeks, not waving but very slowly drowning ever since the traumatic 5-1 defeat at Liverpool. This time last month they were two points clear in the Premier League and still in the FA Cup with a nothing-to-lose last-16 Champions League tie to look forward to. Had they lost here the season would have effectively dwindled away to the familiar playing-for-fourth endgame within the space of eight matches.

In the end the FA Cup was always likely to be Arsenal's most viable option when it comes to tangible signs of progress this season. They are a few players short of a genuine title-challenging squad: probably they need another Mathieu Flamini, another, slightly better Giroud, a season's worth of fit Theo Walcott and another teeth-bearing, finger-pointing Per Mertesacker-flavoured leader in that starting XI.

For now a place in the Premier League top four looks safe, a 3-0 victory in Munich this week the stuff of the surrealist imagination. This, then, was basically Arsenal's season. In spite of which Wenger rested Giroud and started with Yaya Sanogo, who last scored a club goal on 24 May 2013 for Auxerre in Ligue 2 and who was again energetic and eager, without ever suggesting he has the qualities of a top-class striker, but acting quite effectively as an attacking distraction, a Trojan horse of a centre-forward around which Özil buzzed in the opening half-hour.

Özil began in the centre of a tripod of attacking midfielders, with a yen for drifting to the left, from where he scored the opening goal. There was a fast-breaking incision about the move leading up to it, Santi Cazorla's pass putting the German through in the inside-left channel. His finish, a touch to the side then a low early shot, was classily decisive, the celebration muted. Özil had been booed by a section of the Germany crowd in the defeat of Chile in midweek, despite having made the only goal of the game. Some would like Mario Götze to start ahead of him. Who knows, perhaps a little distant pressure might even do him some good. Here he flitted about purposefully, even at times rather surprisingly. Five minutes after the goal Everton broke quickly down the right. But wait. Who was that mysterious last-ditch tackling back-tracker hustling Kevin Mirallas into touch and drawing an ovation from the home crowd? He seemed to be wearing No11. It couldn't be, could it?

It has been a mark of Özil's drooping confidence that too often of late his shark-like bursts of acceleration have come only when he finds himself in possession, a player trying to invent the game around him from a standing start. Here, though, he moved ceaselessly without the ball in the first half, not simply wandering into space and waiting but using the full range of his gymnast's agility to find room for a pass. When Özil plays like this, on a high-rev even without the ball, Arsenal's attack is transformed.

For all that Everton scored an excellent equaliser. Ross Barkley, who was bold and inventive throughout, sprinted 50 metres through an unpatrolled midfield, Mirallas and Romelu Lukaku combining to convert his cross. For a while after that Özil retreated into himself . The doomed, decelerating sprint down the left wing has been a feature of his recent struggles and he looked for a while like a man on the verge of one of his familiar battery-fades, before the appearance of Giroud for the last 25 minutes turned the match. Oxlade-Chamberlain, who was also excellent, won the decisive penalty, drawing just enough contact from Gareth Barry as he bundled past him. Mikel Arteta scored from the spot and that was pretty much that. Everton played well and were hard done by the scoreline. Arsenal, two matches away from avoiding that lurking 10-year mark without a trophy, will hope this is the start of another spring bloom.