Frank Lampard made a winning start to his Everton reign as Brentford were beaten 4-1 in the FA Cup fourth round, while non-league Kidderminster were seconds away from causing a huge upset before West Ham escaped with a 2-1 victory on Saturday.
Lampard was hired on Monday to replace the sacked Rafael Benitez and Everton welcomed the former England star to Goodison Park by winning for just the second time in seven games.
Back in the dug-out for the first time since being dismissed by Chelsea in January 2021, Lampard watched as Yerry Mina headed Everton's opener in the 31st minute.
Richarlison doubled Everton's advantage from Allan's pass three minutes after half-time, with Brentford reducing the deficit through Ivan Toney's 54th-minute penalty.
Lampard was punching the air in delight eight minutes later when Mason Holgate headed in Demarai Gray's corner.
Everton fans serenaded him with chants of "Super Frankie Lampard" before Andros Townsend bagged their fourth goal in stoppage-time.
The buoyant mood was a far cry from the toxic atmosphere during the unpopular Benitez's brief spell.
"I can only thank the fans for their support of me from the moment I walked out and of course at the end, seeing the team perform the way it did," Lampard said.
"It's a day I'll never forget, it was very special, and I can't help but get caught up in the emotion of that for the moment."
Sixth-tier Kidderminster sit 113 places below West Ham, who are pushing for a place in next season's Champions League.
But the minnows were good value for Alex Penny's early goal at Aggborough, the defender smashing home after West Ham failed to deal with Omari Sterling's free-kick.
Moments away from a stunning exit, David Moyes' men were saved by Declan Rice as the England midfielder charged forward in the first minute of stoppage time, cut inside and fired into the roof of the net.
A penalty shootout was looming in extra time until Jarrod Bowen tapped home from close range with virtually the last kick to finally end Kidderminster's brave challenge.
Chelsea also needed extra time to scrape past Plymouth as the League One team missed a late penalty in the Blues' 2-1 win at Stamford Bridge.
The European champions were without manager Thomas Tuchel, who tested positive for coronavirus, and Macaulay Gillesphey nodded Plymouth into a shock lead after just eight minutes.
Cesar Azpilicueta's inventive finish levelled just before half-time, yet Chelsea had to wait until the end of the first half of extra time to go in front when Marcos Alonso slotted home.
Plymouth were awarded a penalty with seconds to go, but Kepa Arrizabalaga ensured there would not be a shoot-out as he saved Ryan Hardie's spot-kick.
In a clash between the leaders of the Premier League and the Championship, Manchester City recovered from Fulham's opening salvo to run out 4-1 winners.
Fabio Carvalho, linked with a move to Liverpool, put second-tier Fulham ahead in the fourth minute at the Etihad Stadium.
But that shock served to inspire City and they equalised immediately through Ilkay Gundogan before John Stones headed the hosts into the lead.
City's Algerian winger Riyad Mahrez converted a 53rd-minute penalty and netted again four minutes later to seal the victory.
There was no transfer window hangover at Tottenham as Harry Kane starred in a 3-1 win against Brighton.
Tottenham boss Antonio Conte had complained that his club made "mistakes" in their January dealings, with four players leaving and only Juventus pair Dejan Kulusevski and Rodrigo Bentancur arriving.
Kulusevski and Bentancur were on the bench as Kane put Tottenham ahead with a curler from the edge of the area in the 13th minute.
Solly March deflected in Emerson Royal's cross to double Tottenham's advantage before half-time with an own goal.
Yves Bissouma reduced the deficit in the 63rd minute, but Kane poked home from on the goal-line three minutes later.
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