The Gunners will now be confident of hauling back Chelsea in the race for fourth place after coming so close to reaching the quarter-finals of the Champions League

Arsenal travelled to Germany with very little hope of getting any sort result against Bayern Munich but fly home with their heads held high after an impressive 2-0 win.

The Gunners have been eliminated from the Champions League on away goals but all the pre-match talk suggested it would be a far more severe outcome, and there are plenty of positives for Arsene Wenger and his men to concentrate on during the flight back to London.

They had Bayern Munich on the ropes in the final 10 minutes of the tie, something that was unimaginable three weeks ago when a demoralised Arsenal team scampered off the pitch after giving up the first leg with barely a whimper.

Wenger’s men had been written off by all observers. They were without the talismanic Jack Wilshere and came up against a side who were widely regarded as one of the favourites to win the Champions League.

A 3-1 lead looked unassailable and Arsenal had had three weeks to realise how little everybody believed in them.

But they had Jupp Heynckes and his men on their toes until the very final whistle after putting in a performance that nobody expected.

Wenger enjoyed a rare night, in recent months at least, where he actually enhanced his reputation.

The Frenchman made two big calls in his team selection for which he deserves massive credit. Regular first-team goalkeeper Wojciech Szczesny and club captain Thomas Vermaelen were both dropped after weeks of questionable performances.

The two players that came in, Lukas Fabianski and Laurent Koscielny, were two of the star performers on the night. The Poland international keeper was hauled into action for the first time in 13 months and rose to the occasion to walk away with a well-earned clean sheet. The French defender, on the other hand, turned in a fine display, was quick and decisive in his defensive work and rose magnificently to head in the second goal late on.

Wenger was brave with his decisions, a bravery which was also evident in the performance of his players.

A potential comeback suddenly became a reality as early as the third minute. Olivier Giroud turned home Theo Walcott’s low cross to give the 3,000 travelling supporters something to believe in.

Bayern fans were stunned and didn’t really know how to react, their team plunged forward in numbers but could not muster the same clinical edge from the first leg.

Arsenal held on valiantly as Bayern upped the ante after the break. Keiran Gibbs and Carl Jenkinson personified the concentration and application of Wenger’s men. The two Englishmen in particular provide a lot of hope for the Gunners defence, which has been under par too many times this season.

The Gunners weathered the German storm and set up a nervy finish for the hosts. Koscielny cannoned in a header to level the tie at 3-3 but it was too little too late as a third goal evaded them, not least because of a poor free kick and two silly fouls from Mikel Arteta.

But the win did restore the reputation of Wenger and his side. The increasingly maligned Gunners boss made the right calls in terms of personnel and tactics and showed he is capable of making decisions in big games.

Although Arsenal are five points behind fourth-place Chelsea on the domestic front, the win against Bayern is a reminder to everybody, the players included, of what they are capable of and what is expected of them. Their season is not over yet.

Football results have a funny way of greying the absoluteness of mathematics. With this most unlikely of European victories, the five-point gap to the Blues, which had looked a chasm before kick-off in Bavaria, now looks eminently bridgeable. Especially with Chelsea fighting on three fronts.

A 2-0 win at the Allianz Arena is a fantastic achievement in its own right, and especially so in these particular circumstances. Wenger’s men played with a nothing-to-lose attitude on Wednesday night, a mindset which will serve them well as they go up against their London rivals for Champions League qualification.

Arsenal have somehow salvaged some desperately needed momentum from what looked a hopeless cause and an increasingly frustrating season. With nine games to go, they must build on this result to ensure they can dine at European football’s top table again next time around.