The Gunners now have just two wins in their last six games in all competitions, both of which came against non-league opposition, to see the pressure grow on under-fire boss Arsene Wenger on another testing afternoon.
On a day that saw contrasting banners fly over the stadium, Wenger's troops conceded to two headed Craig Dawson goals and a close-range Hal Robson-Kanu finish for a rare Albion win over top-seven opposition.
Arsenal now have two weeks to ponder this defeat - the first time they have lost three in succession on their travels since October 2011 and back-to-back losses at The Hawthorns for the first time since the 1950s.
Albion were ahead with the first real opening of the match, making the most of a corner whipped into the box from Nacer Chadli for Dawson to divert into the back of the net.
Dawson's goal, after getting to the ball ahead of Laurent Koscielny, was the 13th West Brom have scored from a corner this term, taking their tally of goals from set pieces under Tony Pulis to over 48%.
The move included 19 passes before the top-class finish from Sanchez, who made the most of a breakdown in communication over defensive duties between Dawson and Chadli to score goal number 27 of the season.
West Brom were largely sitting with six across the backline and looking to make the most of counter-attacks, one of which saw Salomon Rondon drag the ball wide when through on goal.
The first half burst into life once more around 35 minutes in when, in quick succession, Ben Foster kept out Aaron Ramsey on the turn and Petr Cech produced a big stop to keep out Darren Fletcher's volley up the other end.
That would prove to be Cech's final involvement in the contest, though, as he pulled up with a calf injury soon after to be replaced by David Ospina - his first league appearance since last April.
Rondon, without a goal in 13 league and cup games, had a chance to end his barren run when picked out by a teasing Chris Brunt delivery, only to glance wide of the post from close range.
Two minutes later Rondon left the field and headed for the tunnel, seemingly after picking up a knock, and it proved to be a big moment in the match as replacement Robson-Kanu took just 75 seconds and two touches of the ball to make a telling difference.
Ospina could only fumble the ball into the path of the Wales international, who prodded it home to give the Baggies the lead for a second time in the contest, though Arsenal felt that it should have been ruled out as James McClean was stood in an offside position on the line.
Arsenal came within inches of levelling up soon after the hour as Danny Welbeck peeled off Allan Nyom, but he saw his header come back off the frame of the goal on what was just his second Premier League start of the season.
It could just as easily have been game over for the Gunners, though, because WBA countered and, after Robson-Kanu was denied by Ospina, Chadli saw his follow-up strike blocked on the line by Shkodran Mustafi.
The third Albion goal did arrive with 15 minutes left to play, with Dawson again getting his head to the ball first from yet another well-delivered corner - this time from McClean - to put the Gunners on their way to another costly defeat.
A section of Arsenal's remaining contingent of away supporters were quick to make their feelings known at full time, having seen their side once again miss out on the chance to close the gap on the top four.