Capping a miserable week, West Brom was dumped from the FA Cup by Southampton, a 2-1 winner in the fifth round on Saturday.
The latest defeat for the English Premier League's bottom club came after four West Brom players faced a Spanish judge following the alleged theft of a taxi during a training camp in Barcelona.
Also, the club terminated the contracts of chairman John Williams and chief executive Martin Goodman on Tuesday.
Manchester United beat Huddersfield 2-0, Sheffield Wednesday held Swansea to 0-0, and Brighton downed fourth-tier Coventry 3-1.
Wesley Hoedt was unmarked when he gave Southampton an 11th-minute lead, and Dusan Tadic made it 2-0 with a clever chip over West Brom goalkeeper Ben Foster early in the second half.
Salomon Rondon pulled a goal back with a spectacular first-time volley with half an hour left but it wasn't enough to save West Brom.
Manager Alan Pardew gave the captaincy to Gareth McAuley after regular skipper Jonny Evans was one of the four involved in the Barcelona incident, along with Gareth Barry, Jake Livermore and Boaz Myhill.
"I felt I needed to make a little bit of a statement," Pardew said. "I was furious with what happened but at the same time I've got to stay faithful to the players and give them a chance to remedy the situation.
"Gareth Barry was OK today but I thought Jonny was very good in the circumstances. We've had this one crazy evening and it doesn't reflect the work and the professionalism we do as a staff and as players."
Two goals from Romelu Lukaku led United past Huddersfield.
Juan Mata sent Lukaku sprinting clear of the home defense to open the scoring in the third minute and the Belgium striker put the result beyond doubt with a replica goal in the 55th.
There was more VAR (video assistant referee) controversy late in the first half when Mata had a goal disallowed for the most marginal of offside decisions. It took the officials several minutes to rule the goal out, with Mata deemed to have his knee beyond the last Huddersfield defender.
United was without France midfielder Paul Pogba because of illness.
Sheffield Wednesday held Premier League side Swansea as visiting manager Carlos Carvalhal made his first return to Hillsborough since being released by the second-tier team on Dec. 24.
Carvalhal has had a positive effect since joining Swansea four days after his departure from Wednesday, with the Welsh club losing once in 12 games in all competitions on his watch.
The teams will meet again in a replay on Feb. 27 at Liberty Stadium.
"It's a score nobody wants," said Carvalhal. "Maybe in the future, if the managers and referee agree after the first game we can go to penalties, we can finish the game today.
"I believe if you had asked us and the Sheffield Wednesday manager, we'd have gone to penalties."
The last time Brighton was in the top division, it reached the FA Cup final in 1983 losing to Manchester United. Chris Hughton's team joined Man United and Southampton in the last eight with a 3-1 win against fourth-tier Coventry.
Jurgen Locadia, a club record 14 million pounds ($19.6m) signing from PSV Eindhoven in the mid-season transfer window, scored on his debut.
Connor Goldson added a second goal in the first half, and Leonardo Ulloa headed the third in the second half.
Jonson Clarke-Harris gave Coventry's fans something to cheer late in the second.
On Sunday, Tottenham travels to fourth-tier Rochdale while Manchester City visits third-tier Wigan on Monday.
On Friday, Chelsea advanced to the last eight by beating Hull 4-0, and Leicester defeated Sheffield United 1-0.
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