All Whites striker Chris Wood scored a stoppage-time penalty as Burnley beat Barnsley 1-0 to reach the FA Cup fourth round, while League one strugglers Gillingham produced the biggest shock by beating Cardiff 1-0.
Wood came off the bench in the 74th minute to slot home the 92nd-minute winner from the spot at Turf Moor after Barnsley's Liam Lindsay had fouled Matej Vydra.
The 27-year-old has now scored in three consecutive matches for Burnley in all competitions.
Earlier in the match, Burnley had a first-half penalty overturned by the video assistant referee (VAR) for offside.
Vydra was lining up to take the penalty when referee Simon Hooper blew his whistle to review the play, and the VAR showed the Czech international was offside.
"We've pieced together a side, and I'm pleased because that was a good Barnsley side," Clarets manager Sean Dyche told the BBC.
"I felt we had enough to win the game and did enough to win the game, especially at the end of a big, important week for us.
The biggest result of the day happened at Priestfield as Gillingham stunned League side Cardiff City.
Midfielder Elliott List scored the vital goal in the 81st minute, and Gillingham held on in eight minutes of injury time to send Neil Warnock's side out at the first time of asking.
League One Accrington also produced an upset as Billy Kee's goal 14 minutes from time was enough to beat Championship strugglers Ipswich 1-0.
Holders Chelsea and Manchester United, last year's runners-up, booked their places in the fourth round with respective 2-0 victories over Championship sides Saturday.
Elsewhere, Alvaro Morata scored both goals as Chelsea saw off Nottingham Forest at Stamford Bridge while Juan Mata and Romelu Lukaku were on the scoresheet as United beat Reading at Old Trafford.
Brighton, West Ham and Everton also won, but Southampton were held 2-2 at Derby.
Morata, who went into the match having scored just five goals this season, put Chelsea in front four minutes into the second half and doubled his tally 10 minutes later.
United made it five wins out of five under caretaker manager Ole Gunnar Solskjaer thanks to a penalty from Juan Mata and a Romelu Lukaku goal.
Nemanja Matic, Anthony Martial and Paul Pogba were all rested, and Marcus Rashford was left on the bench, while Fred was given a rare start.
And the hosts were far from fluent, offering Reading a number of chances.
But Mata made no mistake from the spot on 22 minutes after he had been fouled and Lukaku rounded the goalkeeper for the second on the stroke of half-time.
Southampton let slip a 2-0 lead to draw 2-2 with Derby, Jack Marriott and Tom Lawrence scoring to force a replay for Frank Lampard's team.
Bournemouth missed a number of early chances and were punished as Brighton ran out 3-1 winners, Anthony Knockaert, Yves Bissouma and Florin Andone scoring the goals.
Arnautovic put West Ham ahead against Birmingham after just two minutes and substitute Andy Carroll secured the win late on.
Arsenal cruised to 3-0 win at Blackpool with a brace from teenager Joe Willock and a third from Alex Iwobi.
Bakary Sako gave West Brom a 1-0 win over Wigan while Peter Crouch equalized in a 1-1 draw for Stoke City at Shrewsbury Town to force a replay.
Swansea, Accrington Stanley, Bolton Wanderers, Middlesbrough, Brentford and AFC Wimbledon also advanced to the fourth round.