Premier League
1 Arsenal 55
2 Man City 53
3 Chelsea 50
4 Liverpool 47
5 Everton 45
6 Tottenham 44
7 Man Utd 40
8 Newcastle 37
9 Southampton 35
10 A Villa 27
11 Stoke City 25
12 Swansea 24
13 Hull City 24
14 Sunderland 24
15 Norwich 24
16 West Brom 23
17 C Palace 23
18 West Ham 22
19 Cardiff 21
The 20-year-old England midfielder - fit again following five months out with a serious knee injury suffered on the first day of the season - finally ended Palace's stubborn resistance when he chipped in a fine pass from Santi Cazorla just after the restart.
After Cameron Jerome's diving header was saved by Arsenal keeper Wojciech Szczesny, Oxlade-Chamberlain struck again to make sure of victory when he combined with Olivier Giroud before running clear to beat Julian Speroni after 73 minutes.
Arsenal now move two points above Manchester City, who host third-placed Chelsea on Monday night, while the Eagles remain in a dogfight for survival, just a point above 18th-placed West Ham.
Earlier, West Brom held Liverpool to a 1-1 draw at the Hawthorns as substitute Victor Anichebe punished Kolo Toure's careless error.
Daniel Sturridge opened the scoring midway through the first half with Liverpool's first effort of the game on target, guiding home a Luis Suarez cross from close range after some intelligent play between Philippe Coutinho and Raheem Sterling.
Suarez then saw his free-kick curl inches away from the post with Ben Foster rooted to the spot before Zoltan Gera fired wide at the other end in a relatively low-key opening 45 minutes.
Pepe Mel's side made a lively start to the second half, with Gareth McAuley drawing a fine one-handed save from Simon Mignolet.
Suarez then came close to doubling Liverpool's lead after getting the better of Diego Lugano and audaciously beating McAuley, but Foster was on hand to deny the Uruguayan.
The visitors looked to be on course for their second Premier League victory of the week but Toure's loose ball across goal was seized upon by Anichebe who lashed past Mignolet into the bottom corner to secure a valuable point.