Making his first league start since the season's opening day, Oxlade-Chamberlain scored both goals in the second half to send Arsenal two points above Manchester City, who host third-place Chelsea on Monday.
The result got Arsene Wenger's side back to winning ways after the 2-2 draw at Southampton that cost them top spot, while Palace were left one place above the relegation zone after a first defeat in three league games.
With Oxlade-Chamberlain in central midfield alongside Mikel Arteta, Arsenal quickly assumed control at the Emirates Stadium, but they struggled to make inroads against Tony Pulis's well-drilled Palace.
The visitors had new goalkeeper Wayne Hennessey on the bench, but their current No1, Julian Speroni, seemed determined to stake a claim to the jersey.
He produced two excellent saves to thwart first Nacho Monreal and then Laurent Koscielny, before bravely diving at Bacary Sagna's feet shortly before half-time.
It had been a disciplined and hard-working display from Palace, but two minutes into the second half they fell behind.
Former Arsenal striker Marouane Chamakh allowed Oxlade-Chamberlain to run into the box behind him and when the scheming Santi Cazorla picked out the England man with a dinked pass, he coolly lifted the ball over Speroni.
Arsenal goalkeeper Wojciech Szczesny was quickly called into action at the other end, saving a header from Cameron Jerome at point-blank range, but Oxlade-Chamberlain's second goal in the 73rd minute settled the game.
The powerful 20-year-old, nicknamed 'The Ox', played a slick one-two with Olivier Giroud before cutting into the Palace box from the left and letting fly with a low drive that Speroni could not keep out.
Liverpool were seeking to move four points clear of fifth-place Everton and they took the lead through Daniel Sturridge at The Hawthorns, only for Toure to gift West Brom a 67th-minute equaliser by passing the ball straight to Victor Anichebe.
The Nigeria striker accepted the gift to level the scores, leaving Liverpool with only a two-point cushion in fourth place and lifting Pepe Mel's West Brom a point clear of the relegation places.
Liverpool manager Brendan Rodgers refused to criticise Toure, saying: "He is a wonderful player. He probably should not have received the ball in the first place.
"I will never criticise any player, especially a defender. We have won many games and played outstanding football, and key to that is constructing from the back."
Rodgers kept faith with the team that had crushed Everton 4-0 in mid-week and he saw his side take a 24th-minute lead when Sturridge volleyed in Luis Suarez's cross from close range.
West Brom suffered a blow when centre-back Jonas Olsson had to limp off four minutes before the break, but a half-time shift to a 4-4-2 formation gave them fresh impetus.
Zoltan Gera had gone close shortly before the interval and it took a stunning one-handed save from Liverpool goalkeeper Simon Mignolet to repel Gareth McAuley's header early in the second period.
West Brom goalkeeper Ben Foster kept his side in the game by blocking from Suarez in a one-on-one situation and less than ten minutes later, the hosts drew level.
Côte d'Ivoire centre-back Toure did not appear to see Anichebe lurking outside the Liverpool box and his attempted pass to Jon Flanagan was cut out by the former Everton man, who lashed home a low shot from just inside the area.