It was inconceivable, in the immediate aftermath of the 3-0 defeat by Manchester City in November that left Arsenal abashed and adrift, that spring would bring a Champions League semi-final against Manchester United. Even more improbable was that Arsène Wenger’s side would go into such a tie not just hoping they can beat United, but genuinely believing it.

Ten points off the pace in the Barclays Premier League, Arsenal’s position obscures how good they have been in the second half of the season. They are unbeaten in the league since that loss to City and are growing stronger. This was a comprehensive victory achieved with a makeshift defence and a second-choice goalkeeper.

Reinforcements at the back, but more important were the deep reserves of self-assurance that Arsenal called on to attack throughout when they needed only a goalless draw to progress. Whether or not the injured masses recover in time for the FA Cup semi-final on Saturday, Arsenal can feel optimistic about beating Chelsea at Wembley and maintaining their progress. While inexperience always carries the risk of volatility, Wenger’s young players are developing consistency and momentum.

“We have confidence and that is down to the slow progress accumulated from game to game in the league,” the Arsenal manager said. “Confidence transfers from one competition to another.”

And perhaps from one team to another, with United unstable just as Arsenal make real Wenger’s prophecies about his team’s potential, turn his nebulous talk of mental strength into tangible results.

Chelsea’s sleepy performance in the first half of their second leg against Liverpool the previous evening was a 150-decibel siren screaming the risks of a cautious approach when a win on the night is not necessary, and Wenger had underlined pre-match that his side needed to be progressive. That psychology was also practical, given the strain on Arsenal’s defensive resources. Bacary Sagna was a late withdrawal because of a virus — more disruption to a defence without William Gallas, Johan Djourou, Gaël Clichy and Manuel Almunia. Robin van Persie did at least pass a fitness test and was preferred to Denilson, confirming Wenger’s attacking intent. It transpired that the only dubious defenders on the pitch were wearing yellow. Without Marcos Senna, their injured star, Villarreal struggled to resist the force of Arsenal’s flair.

The opening goal after ten minutes was direct yet subtle, obvious but ingenious. Cesc Fàbregas’s fabulous back-heel helped Emmanuel Eboué’s pass to bisect the Villarreal back four, Walcott ran clear and coolly clipped the ball over Diego López. Pleasingly for England, the winger’s pace made Joan Capdevila, Spain’s left back at Euro 2008, look anything but a champion. “His finishing is now calm,” Wenger said of Walcott.

Robert Pires, a substitute in the 1-1 draw at El Madrigal, started here against the team he served with distinction before making the mistake of ageing at a club managed by a man as obsessed with eternal youth as Oscar Wilde’s Dorian Gray.

Pires was warmly welcomed by the fans. The chants in his honour represented nostalgia for the triumphant Arsenal of the past, but, with the present crop so vibrant and rampant, the sentimentality was not wistful. Why mourn a lost era when a new one is coming?

Last week in Spain, Adebayor made executing a bicycle kick look as easy as riding a bike, so it was curious that in the first half last night the striker seemed flummoxed in front of goal. The most glaring failure came when a Van Persie free kick was palmed to him by López. Adebayor should have found the net but miscued his header, which was almost bundled in by the stumbling Pires before Gonzalo Rodríguez slammed the ball into the distance from under the crossbar.

The pattern of play did not alter in the second period and Adebayor rediscovered his lethal edge on the hour. Fed expertly by Van Persie, the Togo striker’s touch was perfect and provoked a celebratory dance with more rhythm than anything the Spanish side had managed. Even Wenger jigged with joy.

Nine minutes later, all doubt was removed. Walcott was too tricky for Diego Godín, who felled him in the area. Sebastian Eguren received a second yellow card for his overly passionate protests and Van Persie’s spot-kick was true.

Arsenal (4-4-1-1): L Fabianski - E Eboué, K Touré, M Silvestre, K Gibbs - T Walcott (sub: Denilson, 77min), A Song, F Fàbregas, S Nasri - R van Persie (sub: A Diaby, 77) - E Adebayor (sub: N Bendtner, 83). Substitutes not used: V Mannone, Eduardo da Silva, C Vela, A Ramsey. Booked: Silvestre.

Villarreal (4-2-3-1): D López - Á López, G Rodríguez, D Godín, J Capdevila - S Eguren, B Soriano (sub: N Kahveci, 64) - Cani (sub: Jordi, 70), M Fernández (sub: A Ibagaza, 64), R Pires - G Rossi. Substitutes not used: S Viera, J Llorente, J Venta, F Fuentes. Booked: Eguren, Cani, Godín. Sent off: Eguren.

Referee: W Stark (Germany).

Semi-finals

Barcelona v Chelsea
First leg to be played on April 28, second leg on May 6

Manchester United v Arsenal
First leg to be played on April 29, second leg on May 5

Final Stadio Olimpico, May 27