Ole Gunnar Solskjaer's side, who had won their last ten away games in the Premier League, stay third on 27 points, a point behind second-placed Leicester.
Champions Liverpool are five points clear at the top of the Premier League after a 7-0 away hammering of Crystal Palace while Arsenal's troubles continued with a 2-1 defeat at second-placed Everton on Saturday.
Bilic took over the reins at West Brom in 2019 and was tasked with gaining promotion from the Championship to the top flight.
Joint-leaders Tottenham Hotspur and Liverpool both dropped points on a busy day of English Premier League action as Leicester City and Southampton narrowed the gap in what is shaping up to be one of the most open title races for years.
Images from the football matches played across Europe on Tuesday.
Manchester United remain winless at home in the league this season after Arsenal enjoyed their first win at Old Trafford
Dean Henderson arrived at the club from Carlisle United at the age of 14,
Images from English Premier League matches played on Sunday.
Images from English Premier League matches played on Sunday.
Arsenal's defence of the trophy ended with something of a whimper as Mikel Arteta's side struggled with repeatedly sloppy defending.
Brighton & Hove Albion scored three times in the second half to fight back from two goals down and beat Manchester City
Liverpool frustrated as they were forced to settle for a 1-1 draw at Brighton on Saturday
Images from Sunday's action in the Premier League.
Neymar overtook Ronaldo and moved into second place behind Pele on Brazil's all-time goalscoring list after notching a hat-trick in a 4-2 victory over Peru on Tuesday in a World Cup qualifier.
Several Chelsea players have not returned for pre-season training after testing positive for COVID-19, according to reports in British media.
IMAGES from the English Premier League matches played on Sunday.
Bayern Munich wasted a two-goal lead and needed a lucky 82nd- minute winner from Joshua Kimmich to beat Borussia Dortmund 3-2 in Germany's Super Cup on Wednesday and secure their fifth title of the year.
City were due to open their season against Aston Villa and United against Burnley but those games will be moved.
Manchester City's hopes of closing the gap on the Premier League pacesetters were frustrated as they were held to a 1-1 draw at home to lowly West Bromwich Albion on Tuesday.
Arsenal must trust in Arteta, says Guardiola.
Bruno Fernandes struck from the penalty spot in the ninth minute of stoppage time to give Manchester United victory at Brighton & Hove Albion in the Premier League on Saturday after an incredible finale.
Cristiano Ronaldo scored twice as Juventus strolled to a 3-0 home win over bottom side Crotone in the Italian Serie A on Monday, with the victory taking the champions up to third in the standings.
IMAGES from the English Premier League matches played on Sunday.
Tottenham Hotspur missed the chance to move up to provisional fourth place in the Premier League after relegation-threatened Newcastle United held them to a 2-2 draw with a late equaliser from substitute Joe Willock at St James' Park on Sunday. Images from EPL matches played on Sunday.
Brentford will go into the playoffs along with Fulham and Cardiff City but in a huge swing in fortunes, Nottingham Forest missed out on goal difference with Swansea City grabbing the last slot in astonishing fashion.
Leeds United were crowned champions of the second-tier Championship after third-placed Brentford lost 1-0 at Stoke City in their penultimate game of the season on Saturday.
City's Guardiola defends Mendy after COVID protocol breach.
An off-key Liverpool were frustrated for a second successive game by struggling opponents as they were held to a 0-0 Premier League draw at Newcastle United on Wednesday.
Liam Delap, the son of former Stoke City defender Rory, scored the opener for Pep Guardiola's side in the 2-1 win at the Etihad Stadium
Solskjaer said he showed faith in his young strikers after allowing Romelu Lukaku to join Inter Milan in August.
IMAGES from the EPL matches played on Sunday.
Chelsea got their Premier League campaign on track after 20-year-old right back Reece James helped them to a 3-1 win at Brighton & Hove Albion with a spectacular goal on Monday.
Aston Villa returned to winning ways in stunning fashion as Ollie Watkins scored twice in a 3-0 away thumping of an abject Arsenal in drizzly north London on Sunday.
Three months after the last ball was kicked, the Premier League emerges from the shadow of the COVID-19 pandemic this week for what will be a 92-match slog to the finish.
The unusual circumstances forced by the COVID-19 pandemic will level the playing field, says Arsenal manager Mikel Arteta
Everton yet to receive clarification after City game postponed: Ancelotti
Footage showed the Leeds players in an open-top double-decker bus, surrounded by a swarming mass of chanting fans enveloped in smoke from flares and fireworks.
Images from the English Premier League matches played on Sunday.
Leeds United returned to the Premier League after a 16-year absence on Friday as West Bromwich Albion's loss at Huddersfield Town guaranteed them a top-two finish in the Championship. Three times English champions, Leeds were relegated from the Premier League in 2004 after hitting financial trouble and being forced to sell a host of big-name players such as Robbie Keane, Jonathan Woodgate and Lee Bowyer.
Champions Liverpool were ripped apart 7-2 at Aston Villa and Manchester United were humiliated 6-1 at home by Tottenham Hotspur on Sunday in one of the most astonishing days of Premier League results.