LONDON — Arsenal rediscovered its attacking potency as Alexis Sanchez's double secured a 3-1 victory over Bournemouth in the Premier League on Sunday.

Theo Walcott was also on target with a header as Arsenal overcame a contentious penalty that Callum Wilson converted in a fiercely fought game at the Emirates Stadium.

Having struggled offensively in recent weeks, Sanchez inspired Arsenal to produce some scintillating attacking play and avoid a third consecutive league draw. Arsenal remains fourth, three points behind leader Chelsea but four points ahead of north London rival Tottenham.

"Even when he looks dead (Sanchez) is still alive and finds the resources to do something special," Arsenal manager Arsene Wenger said. "We started well, but after they equalized we became nervous and that's where you could see the draws played on our mind."

Bournemouth can take heart from a promising attacking display, which was delivered without Jack Wilshere, who was ineligible due to the terms of the midfielder's loan from Arsenal.

"I thought we were very good today, it's very difficult when you go behind early in the game, but the group responded very well, with maturity," Bournemouth manager Eddie Howe said.

"Today when you look at the players we were without, the fact that we managed to produce the performance we did without them shows the quality in the squad."

Arsenal's early intensity forced a mistake from Steve Cook in the 12th minute, as the Bournemouth defender's back pass gifted Sanchez the chance to round goalkeeper Adam Federici and calmly place the ball into the empty net.

Arsenal believed it should have had a penalty two minutes later but referee Michael Jones waved play on as Sanchez went down under a challenge from Nathan Ake. Replays showed that any contact did in fact take place just outside the area.

The home fans were doubly aggrieved in the 25th when Jones awarded the visitors a penalty as Nacho Monreal and Wilson went shoulder to shoulder in the Arsenal box. The Bournemouth forward calmly placed his spot kick into the bottom right corner.

With Arsenal visibly rattled by the equalizer, Bournemouth spurned opportunities to take the lead, most notably when Adam Smith headed narrowly over when unmarked six yards (meters) out.

However, Wenger's side began to rediscover its rhythm as Sanchez twice came close just before halftime, striking narrowly over after a neat exchange with Ozil before rattling the bar with a powerful effort from the right side of the box.

Arsenal began the second half as it ended the first and Monreal went some way to redeeming himself by supplying the cross for Walcott to restore Arsenal's lead in the 53rd after good work from Sanchez and Ozil.

Arsenal threatened to extend its lead on several occasions before substitute Olivier Giroud centred for Sanchez in the 90th to seal a much-needed victory.