* Arsenal beat Sunderland 2-0 with both goals from Alexis Sanchez
* Arsenal had a Sanchez goal ruled out for a handball by Giroud
* Giroud headed just wide after the break
* Sanchez opened the scoring from close range after 72 minutes
* The Chilean doubled the lead with a header
* Arsenal host Everton in final outing, Sunderland visit Chelsea
LONDON, May 16 (Reuters) - Arsenal kept alive their top-four hopes with a 2-0 victory over Sunderland as Alexis Sanchez broke the visitors' dogged resistance with a late double at the Emirates Stadium on Tuesday.
Relegated Sunderland had defended deep and restricted Arsenal to half chances on a frustrating evening for Arsene Wenger's side until Sanchez rode to the rescue, sidefooting home Mesut Ozil's cross after 72 minutes.
Sanchez, who had a first-half effort ruled out after his shot went in off the arm of Olivier Giroud, then doubled the lead with a close-range header with nine minutes remaining.
The victory leaves Arsenal fifth on 72 points, one behind Liverpool and three behind third-placed Manchester City ahead of Sunday's final round of fixtures to decide who will join Chelsea and Tottenham Hotspur in next season's Champions League. (Reporting by Toby Davis; editing by Martyn Herman)