- 1. FC Köln
Manchester City roared back from a two-goal half-time deficit to score three times after the break.
Manchester United slipped to their first domestic defeat under Ole Gunnar Solskjaer at Arsenal.
Palace won 2-0 away to third-tier Doncaster Rovers, the lowest league club still in the competition, while Wolves beat Championship side Bristol City 1-0.
Rafael Benitez's side were seconds away from a valuable victory after Isaac Hayden's first goal since 2017.
Mohamed Salah's 11th goal of the season was a classy one and helped subdue a dangerous Wolves side who had made a lively start.
Chelsea are currently in fourth place, 10 points adrift of Premier League leaders Manchester City after 15 games.
Henrikh Mkhitaryan, introduced as a 76th-minute substitute, floated a cross into the Wolves penalty area that evaded everyone before drifting in at the far post.
Jose Mourinho was concerned by what he saw as his team's poor attitude as he came close to suffering consecutive home league defeats for the first time in his career.
Alex Ferguson's emotional return to Manchester United for the first time since his life-saving surgery was spoiled as Wolves snatched a 1-1 draw at Old Trafford on Saturday.
City were good value for their point but they looked unusually vulnerable against Nuno Espirito Santo's well-drilled side.
Pedro headed in after 65 minutes following an intricate build-up from Chelsea, while Diego Costa scored in the 89th minute to help his side seal a place in the quarter-finals
The project is part of the West Bromwich Albion Foundation programme in association with Youth Football International (YFI) to scout, train and develop talent across the country. Selection trials will take place on January 18 at the Ambedkar Stadium.
Uruguay forward Luis Suarez struck twice early in the first half at Anfield and completed his treble soon after half-time.
Meanwhile Wenger felt compelled to admonish Arsenal's Jack Wilshere after the England midfielder was spotting holding a cigarette outside a London nightclub in midweek -- although the player himself insisted this was a "prank" and that he wasn't a smoker.
Following hot on the heels of last weekend's chastening 4-1 defeat at local rivals Manchester City, it loads further pressure on Moyes, who succeeded the legendary Alex Ferguson as manager in July.
Before the match, United manager Moyes referred to last Sunday's humbling 4-1 defeat at Manchester City as "embarrassing" and just four players that started that game were in the Scot's line-up for the West Brom clash.
Steve Clarke's side held on for victory, to leave Moyes with a dismal return of three defeats, one draw and only two victories from his first six league matches. United's fans could nonetheless take a small crumb of consolation from the fact that their conquerors from last weekend fell to a 3-2 defeat at Aston Villa.
Van Persie, last season's top scorer in the English Premier League, has missed recent matches against Manchester City and Liverpool but has returned to training.