Marc Guehi scored his first goal for Manchester City to seal a 2-0 win over minnows Salford in the FA Cup fourth round, while Burnley suffered an embarrassing exit against Mansfield on Saturday.
Pep Guardiola's side took an early lead through Alfie Dorrington's own goal, but they made hard work of seeing off their fourth-tier opponents at the Etihad Stadium.
There were only nine minutes left when City defender Guehi delivered the decisive blow with his maiden goal since signing from Crystal Palace in January.
Owned by Manchester United legends Gary Neville and David Beckham, Salford were playing in the fourth round for the first time in their history.
City beat Salford 8-0 in the FA Cup third round last season, and it took just six minutes to breach the minnows' defence again.
Rayan Ait-Nouri's cross was arrowing towards Omar Marmoush until Salford's Dorrington stuck a leg out and deflected it into his own net.
City fans expecting that to be the trigger for a deluge of goals were disappointed.
Guardiola's men struggled to find any momentum and needed a James Trafford save from Salford striker Ben Woodburn to preserve their lead.
Brandon Cooper wasted a golden opportunity to equalise when he headed wide from Luke Garbutt's corner on the stroke of halftime.
City were unable to muster a single shot on target in the first half and Salford nearly drew level after the interval when Kelly N'Mai's fierce strike was parried by Trafford.
Guehi finally ended Salford's resistence in the 81st minute, tapping in after Matt Young palmed Rayan Cherki's pass into his path.
At Turf Moor, Mansfield's 2-1 win over Premier League strugglers Burnley took them into the fifth round for the first time since 1975.
Burnley went into the game bolstered by their first Premier League win since October over Crystal Palace in midweek, but boss Scott Parker made nine changes and the gamble backfired.
'TIRED LEGS'
Burnley took the lead through Josh Laurent's 21st-minute goal, but Nigel Clough's team, who sit in mid-table in League One, staged an impressive fightback in the second half.
Rhys Oates headed in the equaliser in the 53rd minute and Louis Reed capped a fine individual performance with a brilliant free-kick 10 minutes from fulltime.
Ten-man West Ham edged through as Crysencio Summerville clinched a 1-0 win at third-tier Burton.
Nuno Espirito Santo's side were taken to extra-time before Summerville ended the underdogs' stubborn resistance with his sixth goal in his last seven games in all competitions.
West Ham's Freddie Potts was sent off soon after Summerville's strike in the first period of extra-time, but the Premier League strugglers held on to survive a gruelling fourth-round clash.
"We knew Burton would come on strong, every throw-in and every set-piece is a situation that requires maximum attention and the players did well in that aspect," Nuno said.
"There were some tired legs in extra time and Summerville helped us out. He is doing a good job."
With their team three points from safety in the Premier League, the Hammers' erratic display will hardly ease fans' fears about their chances of avoiding relegation.
West Ham supporters flew a plane over the Pirelli Stadium with a banner calling for David Sullivan and Karen Brady to sell the club, while supporters inside the stadium chanted "sack the board".
Nuno made 10 changes as he prioritised West Ham's fight for top-flight survival.
Summerville struck in the 95th minute with a dynamic break down the left flank before smashing a deflected strike into the top corner from the edge of the area.
West Ham substitute Potts was dismissed for a reckless lunge on Julian Larsson in the 101st minute.
Later on Saturday, Liverpool meet Brighton at Anfield and Aston Villa face Newcastle.