Nuno made three changes from the West Ham side which went down 3-2 to Southampton in their last home game, and they all impacted the game.
Konstantinos Mavropanos missed out after picking up a knee problem against the Saints with Golambeckis drafted in at centre-back, while Edvin Austbo replaced Manor Solomon and Pablo was handed a start in place of Taty Castellanos.
West Brom’s James Morrison made two changes from the XI which drew 1-1 at Preston, with Rabby Nzingoula replacing Harry Whitwell and Morgan starting in place of Barney Stewart – that too, proved key.
Nuno spoke to his West Ham players during the week about starting games quicker, but while they won a corner after just 16 seconds the pace soon dropped off.
It was the visitors who looked more threatening on the break and they went ahead when Price’s wonderful curling through ball sent Morgan racing into the box on the right and he unselfishly opted to put it on a plate for Horn Myhre in the middle, rather than have a shot himself.
Price might have had another within two minutes as the Hammers defence looked shaky again allowing Morgan to dart in.
But though he picked out his unmarked team-mate near the penalty spot, Price stumbled at the crucial moment and skewed his shot wide.
Boos rained down from the home fans and even more followed when Mads Hermansen hoofed the subsequent goal-kick clean out of play.
Those jeers turned to cheers when Mohamadou Kante spun and swept a first-time pass out to Bowen and the Irons skipper drove into the box, before lashing in a low cross-shot which took a slight deflection off Callum Styles and beat Max O’Leary via a kiss off the inside of his near post.
Bowen pointed to his temple in the celebrations, urging the fans to focus, but his team-mates were left lacking on that front three minutes into the second half when Price was given space to curl in a cross from the left.
Golambeckis tried to cut out the outswinger but missed the ball which was cushioned neatly by Horn Myhre to Morgan in the space behind the defender. Morgan steadied himself and slotted across the keeper and inside the far post.
The home side tried to mount a comeback. Divine Mukasa watched an 18-yard shot deflect wide off Chris Mepham and the subsequent corner was met by the head of Max Kilman, only for O’Leary to claw his effort round the post.
O’Leary also dived to his left to parry Kyle Walker-Peters’ curling effort after being teed up by sub Solomon.
But the game was effectively up after 73 minutes when a deep Price corner from the left was deflected away tamely by Morato, with the ball falling to Styles 15 yards out to lash home through a crowd, giving the unsighted Hermansen little chance.
The hosts threw on Castellanos for Golambeckis in the closing stages, but the Argentine could only lash one effort off target, while an acrobatic effort in added time was straight at O’Leary.