After last weekend’s victory over Bolton Wanderers, Arsène Wenger called on Cesc Fàbregas and Tomas Rosicky to score more goals. Having found the net on Saturday, the midfield pair did so again last night as Arsenal all but guaranteed a place in the Champions League next season.

Five days ago, Wenger’s team looked in mild peril of dipping into the Uefa Cup. Now they are third in the Barclays Premiership. Liverpool can leapfrog back over them with a draw against Middlesbrough tonight, but Arsenal are eight points clear of Everton, who are fifth, with four matches to play. Another two wins and they will have improved on last season’s points total, the lowest since Wenger took charge in 1996.

After last night’s victory over Manchester City, the Arsenal manager was enthused about the prospect of individual enhancement. Fàbregas, 20 next month and making his 50th appearance of the season, was this week nominated for the PFA Player of the Year and Young Player of the Year awards. “There is more to come from him,” Wenger said.

“From 19 to 22 you go from a young boy to a man, but even now he can dominate a game. He can develop physically, but he has a big authority on the pitch already.

“When you look at his chances this season you are not surprised he scores, but the longer it goes without a goal, the more difficult it becomes. You could see from the way he celebrated his goal on Saturday that it was an obsession. You could see from the relief that it was a weight off his shoulders.”

Saturday’s stroll against Liverpool had taken City beyond 40 points, the draw extending their unbeaten run to five matches, and the confidence stemming from that sequence seeped through the team as they put Arsenal under pressure despite going behind to an early goal by Rosicky and despite a conservative outlook that led to them putting plenty of men behind the ball when they did not have possession.

“We probably should have got a point,” Stuart Pearce, the City manager, said. “With 60 minutes gone, I am very comfortable [at 1-1] and the fans are booing Arsenal. It is a nice feeling when you are away from home. Then one of their players [Fàbregas] has pulled out a wonder strike. We will go home disappointed — but we will learn from it.”

After 12 minutes, Abou Diaby collected the ball 30 yards out and pushed it wide to Emmanuel Eboué. The right back whipped over a cross that Nedum Onuoha failed to clear and Rosicky volleyed in his third league goal of the season.

Diaby was substituted after he slid into a tackle and was accidentally kicked above an eye by Richard Dunne, the City captain. He was heavily bandaged and briefly tried to play on, but suffered double vision and needed four stitches.

Jens Lehmann is deliberating over whether to extend his contract. The Arsenal goalkeeper’s decision-making was a relevant issue last night, too, as he fluffed a clearance in the 41st minute. Joey Barton intercepted the ball and fed Michael Johnson. He set up DaMarcus Beasley, the United States winger, who finished coolly. City were almost ahead three minutes later when Barton’s run and shot forced Lehmann into a good save.

After the break, Arsenal failed to make the most of several promising positions. In a move that went firmly against Arsenal stereotype, Emmanuel Adebayor latched on to a hopeful long ball and raced clear, but his effort from a tricky angle was saved by Andreas Isaksson. Onuoha then compensated for his earlier dalliance by making a fine block to deny Adebayor and Isaksson was called on again to save a downward header from the Togo striker.

The sense grew that City could emulate West Ham United’s unlikely victory at the Emirates Stadium this month, but, after 73 minutes, the home team finally broke through. A loose ball dropped to Fàbregas, who smacked in a wonderful goal from more than 20 yards.

It was only his second strike since August, when he hit a brace against Dynamo Zagreb in a Champions League qualifier — goals ensuring European football at the start of the season and again at its end.

Seven minutes later, Alexander Hleb jinked into the area and crossed for Júlio Baptista, who had come on for Diaby, to sweep the ball low into the net. Lehmann saved from Georgios Samaras, a substitute, to ensure that a stressful last few minutes were not added to what has been a difficult couple of months.

Arsenal (4-5-1): J Lehmann — E Eboué, K Touré, W Gallas, G Clichy — A Hleb, F Fàbregas (sub: Denilson, 85min), Gilberto Silva, T Rosicky (sub: P Senderos, 90), A Diaby (sub: J Baptista, 30) — E Adebayor. Substitutes not used: M Almunia, J Djourou.

Manchester City (4-5-1): A Isaksson — N Onuoha, R Dunne, S Distin (sub: B Corradi, 78), M Ball — Sun Jihai (sub: G Samaras, 78), D Hamann, J Barton, M Johnson, D Beasley — D Vassell (sub: S Ireland, 90). Substitutes not used: N Weaver, H Trabelsi.

Referee: M Halsey