Robinson’s second-half strike earned the Baggies just their second win in 10 matches and ended a run of 11 league games on the road unbeaten for Fulham.
West Brom manager Bruce named an unchanged side to the one that fought back to rescue a point against Huddersfield Town on Friday. Alex Palmer, who had just returned from an emergency loan at Luton Town, took David Button’s place on the bench.
Story of the match
West Brom started the game on the front foot. Robinson fed strike-partner Karlan Grant away but his strike found only the side netting. Grant then sent in a teasing cross that only narrowly evaded Kyle Bartley.
Marek Rodak was called into action for the first time just before the half-hour mark. Grant fired a half-volley at the Fulham goalkeeper from the edge of the box. In the aftermath, Alex Mowatt went down after having his boot kicked by Harrison Reed, but referee Kevin Friend waved away the appeals.
The Baggies’ frontline continued to link up nicely. Grant was slipped in by Robinson and had a low shot blocked away by Rodak after doing well to fend off the bandaged Tim Ream.
Rodak was again called into action two minutes later. Robinson got on the end of a Jake Livermore pass down the right before cutting inside and firing a left-footed strike at the visiting keeper after Tosin Adarabioyo had slipped.
There was still time for one more chance before the interval. Another Townsend cross from the left was parried away by Rodak, with no Baggies player there to pounce. West Brom went into the break with a roar of approval from the home supporters after a promising 45 minutes.
Albion had the first chance of the second half within a minute. Semi Ajayi headed across goal for Grant, whose header was held by Rodak.
Matt Clarke was needed with three vital interceptions in his own box soon after as Fulham began to put the hosts under their first spell of pressure with Antonee Robinson working into good areas down the left.
West Brom got the goal they deserved on 63 minutes. Grant was allowed too much space in the centre to slot through for Robinson, who made no mistake in slotting into the net for his seventh goal of the campaign.
The visitors had their best chance of the game with seven minutes remaining. Carvalho flashed a low cross for Aleksandar Mitrovic, but the Championship’s record goalscorer blazed over from about eight yards out.
Albion held out in the closing stages to go back into the top half of the Championship table and claim their first victory over Fulham since 2010.
West Brom travel to Bristol City on Saturday, while Fulham are not in action again for three weeks.
West Brom (3-5-2): Johnstone; Clarke, Bartley, Ajayi; Townsend, Livermore (c), Mowatt (Molumby 87), Gardner-Hickman, Furlong; Grant (Diangana 84), Robinson (Carroll 77). Subs: Palmer, O’Shea, Reach, Kipre.
Fulham (4-2-3-1): Rodak; Robinson, Ream (c), Tosin, Williams (Muniz 81); Reed (Cairney 72), Chalobah; De Cordova-Reid (Cavaleiro 72), Carvalho, Wilson; Mitrovic. Subs: Gazzaniga, Tete, Hector, Seri.
Referee: Kevin Friend (Leicestershire).