Arsenal began its FA Cup defence with a 3-1 comeback victory against Sunderland in the third round on Saturday, while Manchester City emphatically defeated Norwich 3-0.
Also, Premier League side Aston Villa was held to 1-1 at fourth-tier Wycombe, while fifth-tier Eastleigh drew 1-1 with second-division side Bolton.
It looked as if there could be a shock at Emirates Stadium, where the Premier League leader fell behind to a Jermaine Lens strike after 17 minutes for Sunderland, which was second-to-last in the league.
But Joel Campbell equalized, then two goals in three second-half minutes from substitute Aaron Ramsey and Olivier Giroud sealed Arsenal's place in the fourth round.
City had no problems at Norwich. Sergio Aguero beat four players before converting for the opener, and assisted on the second scored by Kelechi Iheanacho.
Kevin De Bruyne added the third, shooting though the legs of goalkeeper John Ruddy.
Eastleigh went 1-0 up over Bolton in the second half of its match at its Silverlake Stadium with an own goal by Bolton defender Dorian Dervite, but Darren Pratley saved humiliation by leveling moments from the end.
Villa became the second Premier League side to fail to beat fourth-tier opposition.
Villa captain Micah Richards gave his side the lead in the first half but Joe Jacobson leveled for the Chairboys with a penalty.
Villa was last in the Premier League, and the draw means its winless run stretches to 16 matches. After the game, Richards was on the pitch having an animated discussion with unhappy Villa supporters, and manager Remi Garde accepted the criticism from fans.
"I can understand the fans," Garde said. "They travel a long way...and this is what we deserve."
Liverpool was the first Premier League side held by fourth division opponents on Friday, when it drew with Exeter 2-2.
But its local rival Everton avoided a similar fate against opponents from the same division, as it beat Dagenham 2-0 at Goodison Park with goals from Aruna Kone and Kevin Mirallas.
West Brom needed a last-minute goal from James Morrison to draw with second tier Bristol City 2-2 and earn a replay, while Bournemouth came from a goal behind to beat Birmingham 2-1.
Meanwhile, Southampton lost 2-1 against Crystal Palace, Watford beat Newcastle 1-0, West Ham edged Wolverhampton 1-0, and Stoke beat Doncaster 2-1. Late Saturday, Manchester United hosted third-tier Sheffield United.