Sam Allardyce turned the tables on Tony Pulis with a display of physical, clinical football that gave Crystal Palace another vital three points in their fight against relegation.

Two second-half goals, the first an instant control and finish by Wilfried Zaha, the second a composed one-man counterattack by Andros Townsend, did what West Brom have done to many other sides this season. It need hardly be pointed out however that it is also a habit Allardyce has fostered over his long career as a Premier League manager.

“It’s the start of recovery I would say,” Allardyce argued after the match. “We’ve got back-to-back wins and the performance was good both in and out of possession. What we did out of possession gave us the platform and then we’ve been asking for an addition of quality in the final third and that came today with two moments of outstanding quality. Andros’s goal is the top goal of our season so far and I don’t think anyone will beat it. That win is a great lift for us all. We’ve got the basics in place and we kept their crowd quiet.”

That was not strictly accurate. The crowd was noisy as both set of fans exchanged opposing opinions on the merits of Tony Pulis. The Baggies manager had done his level best to add spice to the occasion, making detailed observations before the match about the money Palace had spent in seasons since he left the club, amounts that looked at odds with their current league position. He had also refused to confirm whether he had paid the £3.7m fine he owed the club for cashing in a loyalty bonus shortly before he resigned from Selhurst Park. “We’re having your house, oh Tony Pulis, we’re having your house,” sang the away support. The Smethwick end matched them lung for lung with “Tony Pulis, we’ve got … Tony Pulis‚” to the tune of Palace’s Glad All Over.

Such noises may or may not have piqued Allardyce, but he insisted his players knew nothing of what their former manager had said. Instead he praised his players for finally sloughing off the anxiety he claims has been haunting their performances so far this season, with the previous Saturday’s 1-0 win over Middlesbrough only the second of Allardyce’s tenure. This week there was no mistaking that Palace were a Big Sam side: strong in the challenge, effective in the cross, every player looked a good 2% stronger than they did a month ago (which, according to Sam’s maths in last week’s Palace programme, ought to make them 22% stronger as a whole).

After defending stoutly for much of the first half, Palace hit Albion with a sucker punch five minutes into the second. Yohan Cabaye received the ball just inside the Albion half with all the play in front of him. He picked out one of his pinpoint quarterback passes straight to Wilfried Zaha on the far side of the Albion box. The winger took one touch on his chest before finishing low with his left foot into the far corner of the net.

Palace sealed the match with five minutes remaining with Townsend’s fine solo effort. It started on the edge of his own area when he robbed the Albion teenager Jonathan Leko, given a rare substitute’s outing by an increasingly desperate Pulis. As Townsend accelerated away on the counterattack. Leko tracked back but was muscled off the ball by the England winger who then threw three stepovers at Gareth McAuley, ran past him and hit another low shot that took a deflection off Jonny Evans and flew past Foster.

Townsend was just one of several rejuvenated figures in the Palace side. Cabaye sprayed his full range of passes since being saved from sitting at the base of midfield by the addition of the Serb Luka Milivojevic. Jason Puncheon rose to the responsibilities of the captaincy, and at the back Mamadou Sakho was superb. The former Liverpool man was cast out from Anfield but held the defensive line at the Hawthorns, making several key interceptions and apparently relishing the physical challenge against Salomón Rondón.

Pulis, for his part, did not entirely roll back on his comments, observing that, in Jeffrey Schlupp, Palace have “a £15m substitute left-back. That’s not bad, is it.” He said he could endure whatever chants fans chose to sing at him but claimed his team had dropped from the high standards they had set for much of this season. “We’ve had an off day, it was an off day,” he said. “Players have to understand they really have to be up for it every game. They’ve been fantastic this year and now have to dust themselves down.”