They had won just one of their last four league games and were aiming to get all three points to move firmly into second place in the league table.
West Bromwich Albion, meanwhile, were 19th in the Premier League table and had won just one of their last 14 games in all competitions. They were looking to get their third league win of the season in a bid to push out of the relegation zone.
Manchester United began the game in their usual sluggish manner and were punished for it when Diagne headed home from close range after some poor defending from Victor Lindelof.
The Red Devils were off the pace and still kept on stroking the ball from flank to flank with no real intent. The hosts got closer to getting the second goal of the game but were denied by a good save from David de Gea.
United finally leveled the scores just before halftime through a brilliant volley from club top-scorer for the season, Bruno Fernandes.
Manchester United showed intent in the second half as they poured men forward in search of the lead. Ole Gunnar Solskjaer's men looked to be finally rewarded for their troubles when Harry Maguire won a penalty but the decision was overturned by VAR.
Manchester United's intensity soon petered out and Sam Allardyce's men got several chances to regain their lead but could not take advantage and the game ended all square.
The result sees Manchester United return to second place on the table, but only on goal difference over third-placed Leicester.
The Red Devils, who were top of the Premier League just weeks ago, now find themselves seven points behind neighbors Manchester City, who have a game in hand.
The result also did little to change West Brom's fate, as they remain 19th in the league, 12 points away from safety.
Manchester United Player Ratings
David de Gea - 5/10
There was nothing he could do about the West Brom opener as it was a first-time header from close range. The Manchester United man did well to remedy a Harry Maguire mistake and prevent the hosts from taking the lead.
Aaron Wan-Bissaka - 5/10
The Manchester United full-back went forward regularly but was guilty of lacking innovation as he kept on turning to pass backwards. The Englishman completed none of his crosses all game.
Victor Lindelof - 4/10
Lindelof was bullied far too easily in the air by the more hungry Diagne who headed home the opening goal for West Brom.
He was lucky that Diagne failed to grab a second when he completely mistimed an interception in the box, allowing the ball to fall to the Senegalese, who could only shoot over.
Harry Maguire - 5.5/10
The captain drove into the box non-stop and even won a penalty for his side, however, the penalty was overturned by the VAR.
Maguire, like his partner, also fell victim to Diagne's constant hassling and allowed the Senegalese through on goal before he was denied by a brilliant De Gea save. He also nearly won the game with a late header saved on to the post by the keeper.
Luke Shaw - 5.5/10
Shaw's development in the final third continued against West Brom as he claimed another assist to his name. He drilled in a brilliant cross into the box for Bruno Fernandes to volley home.
The Manchester United full-back created four chances and completed a game-high six crosses.
Fred - 5.5/10
The Brazilian worked tirelessly all game for Manchester United as he recovered the ball for his side and kept play ticking. He was hauled off after 80 minutes for Donny van de Beek.
Scott McTominay - 5.5/10
McTominay did little wrong all game and was unlucky not to have handed his side the lead in the second-half when his goal-bound strike was cleared off the line by West Brom's Darnell Furlong.
Bruno Fernandes - 6/10
Manchester United's knight in shining armor. The Portuguese got the equalizer for his side with an immaculate volley, sending his weaker left-footed shot into the top corner.
He worked tirelessly all game but his teammates all looked a level below him for most parts of the game.
Marcus Rashford - 5/10
The Manchester United forward once again seemed to lose sight of what was important and constantly looked to dazzle at the expense of his team. He completed a game-high four take-ons but failed to produce anything noteworthy for the visitors.
Anthony Martial - 4/10
Martial was once again non-existent. He looked a shadow of himself from last season and had no meaningful impact on the game. He had no shot and created no chance before he was replaced by Mason Greenwood in the 66th minute.
Edinson Cavani - 5/10
The veteran striker was starved of chances and was isolated for most of the game as the West Bromwich Albion defenders did well to ensure he was marked out all game.
Player ratings for the Manchester United Substitutes
Mason Greenwood - 5.5/10
The 18-year-old was substituted on for the final 24 minutes of normal time and was simply electric as he injected new life into the Manchester United attack. He had more shots, created more chances, completed more take-ons and crosses in less than half an hour than Anthony Martial, who he came on for. An immediate impact.
Donny van de Beek - 5/10
Ole Gunnar Solskjaer's last gasp attempt to salvage a win the Dutchman had no noteworthy impact on the game.