The Czech Republic midfielder claimed his second five minutes into the second half, ramming home at the second attempt after Foster blocked his initial attempt from the edge of the box.
Mertesacker's mistimed lunge granted West Brom a lifeline that Morrison duly grasped with 19 minutes left, but Arsene Wenger's side survived a late onslaught from the home side as they closed to within a point of third-place Tottenham Hotspur.
"We now we have one target - to win our games,'' said Arsenal manager Wenger.
"Then we do not have to look at Tottenham or at Chelsea. If we lose our games, you have always to look at the results of the others.''
Meanwhile, Matthew Lowton and Christian Benteke scored potentially crucial late goals to give Villa a 3-1 win at Stoke City that lifted Paul Lambert's team out of the relegation zone and drew the hosts into trouble.
Gabriel Agbonlahor converted at the near post from Lowton's right-wing cross to give Villa a ninth-minute lead, only for Michael Kightly to equalise for Stoke in the 80th minute.
However, with time running out, Lowton launched a magnificent 30-yard volley into the top-left corner in the 87th minute before Benteke added a third to send Villa three points clear of the bottom three.
Stoke, who have won just once in 13 games, are one point better off in 14th place.
"I don't think you will see a better goal in Europe, let alone anywhere else, than Matt Lowton's,'' said Villa manager Lambert.
Reading's hopes of avoiding relegation were seriously compromised after a 2-0 loss at home to manager Nigel Adkins's former club Southampton left them eight points from safety with only six games remaining.
"We needed a win today,'' Adkins said.
"We were up against a good team but we're at home and we've got to win the game of football.''
Southampton, meanwhile, are now seven points above the bottom three after their third consecutive victory and appear poised to secure their status among the elite for a second season.
Elsewhere on Saturday, Norwich City were denied only a second win in 15 games in an entertaining 2-2 draw at home to Swansea City.