The Czech midfielder's first Premier League goals of the season push Arsene Wenger's side into fourth but Per Mertesacker's late red card meant they had to do it the hard way
Clinical strikes either side of the break from the Czech midfielder had given the Gunners a comfortable lead but Per Mertesacker’s 70th-minute sending off and James Morrison’s subsequent penalty made for a frantic finish.
Arsenal managed to hold on, though, and their fifth successive victory at the Hawthorns sees Arsene Wenger’s side move into fourth, with Chelsea and Tottenham not due to play until tomorrow.
Steve Clarke made just two changes from his side’s 3-1 defeat at West Ham last week as Morrison came in for the suspended Youssouf Mulumbu and Jerome Thomas replaced Romelu Lukaku.
The visitors, meanwhile, named an unchanged side from their 4-1 win against Reading as Gervinho and Olivier Giroud retained their places up front in the absence of the injured Theo Walcott.
It was no surprise to see Arsenal dominate possession early on, though it was the home side that came closest in the early exchanges as a Claudio Yacob header was cleared off the line by Rosicky.
But it was back to business as normal when Gervinho made a fine run into the West Brom penalty area and crossed for the Czech midfielder, whose header into the bottom corner this time made him the hero at the other end. It was the Ivorian’s third assist in two matches and Rosicky's first league goal of the season.
Chris Brunt then tested Lukasz Fabianski with a low free kick but, in truth, things were looking very easy for the Gunners.
And Wenger's side should have doubled their lead on 42 minutes after great work from Giroud and Santi Cazorla teed up Aaron Ramsey. The Welshman somehow managed to skew his shot wide from just yards out, however, for what was in the end an embarrassing miss.
It remained 1-0 at the break but the Gunners were quick to add a second after the restart – and it was that man Rosicky once again.
Crossing in from the right, Ramsey managed to atone for his earlier error with a fine ball and there was a glint in the Czech’s eye as he sent home the rebound after first thumping a half-volley at Ben Foster in the Baggies goal.
But with 20 minutes left, disaster struck for the visitors as a long ball over the top released Shane Long and Mertesacker brought him down in the danger area. A penalty was subsequently awarded and the German defender received his marching orders.
Morrison duly dispatched the spot-kick to register his first home goal since October and Wenger responded swiftly with a defensive change, bringing captain Thomas Vermaelen on for Gervinho.
With the man advantage, the Baggies pushed forward and Gareth McAuley and substitute Lukaku both fired agonisingly wide within minutes of each other.
And Long then came even closer at the death – but Wenger’s men held on.