Tony Pulis' West Bromwich Albion tenure began with a 7-0 demolition of non-league Gateshead in the FA Cup third round on Saturday, while Leicester City eliminated managerless Newcastle United.
Pulis was appointed as West Brom's new head coach on New Year's Day following Alan Irvine's sacking and he watched his new charges cruise into round four, with Saido Berahino scoring four times.
The England Under-21 striker, who has been linked with Liverpool, opened the scoring in the 42nd minute at The Hawthorns before Victor Anichebe added a second with a solo goal in first-half injury time.
Berahino produced two classy finishes early in the second period to complete his hat-trick, with Chris Brunt and James Morrison adding two more goals before Berahino struck again to take his tally for the season to 13.
While West Brom began their new era in confident fashion, Newcastle made a forgettable start to life without Alan Pardew, who had been confirmed as Crystal Palace's new manager earlier in the day.
With Newcastle coaches John Carver and Steve Stone deputising in the dug-out, Leicester prevailed in the day's only all-Premier League tie courtesy of a 39th-minute header by Argentine striker Leonardo Ulloa.
Swansea City joined Leicester in the fourth round after a 6-2 romp at fourth-tier Tranmere Rovers.
Bafetimbi Gomis claimed a brace for Garry Monk's visitors, while Nathan Dyer, Tom Carroll, full debutant Mo Barrow and Wayne Routledge also found the net.
Blyth Spartans of the seventh-tier Northern Premier League looked poised to record the day's biggest upset after going 2-0 up at home to second-tier Birmingham City thanks to a double from captain Robbie Dale.
The scoreline even attracted the attention of former Portugal and Real Madrid great Luis Figo, who began to follow Blyth's official Twitter account via his @LuisFigo page.
But three goals in six minutes turned the tie on its head, with Lee Novak reducing the arrears in the 52nd minute before Wes Thomas claimed a quick-fire brace to give Birmingham a 3-2 win.
The day's biggest upset came at third-division Rochdale, who beat two-time cup-winners Nottingham Forest of the Championship 1-0 thanks to a 12th-minute spot-kick by Peter Vincenti.
Meanwhile, Derby County, currently third in the Championship, needed an injury-time penalty by Chris Martin to see off fifth-tier Southport 1-0.
Holders Arsenal host Hull City on Sunday in a repeat of last season's final, which the north London club won 3-2 to end a nine-year trophy drought, and there are three other repeats of former finals in the third round.
Sunderland host Leeds United (1973) on Sunday, with Tottenham Hotspur visiting Burnley (1962) the following day.
Meanwhile, Liverpool visit AFC Wimbledon on Monday in a match that recalls the original Wimbledon's shock success in the 1988 final.
Premier League co-leaders Chelsea and Manchester City both enter the competition against second-tier opposition on Sunday, with Chelsea hosting Watford and City entertaining Sheffield Wednesday.
Palace travel to fifth-tier Dover Athletic for their first game since Pardew was appointed manager.
Manchester United visit third-tier Yeovil Town, while the fourth and final all-Premier League fixture sees Everton host West Ham United on Tuesday.