Holders Arsenal, winners of the FA Cup in three of the past four seasons, have been bundled out in the third round, beaten 4-2 at Championship side Nottingham Forest.
Eric Lichaj scored twice while Ben Brereton and Kieran Dowell scored Forest's other goals to knock Arsenal out in round three for the first time since 1996.
Tottenham Hotspur scored three goals in eight minutes on Sunday as they clinched a 3-0 win over AFC Wimbledon but West Ham will have to replay after being held to a 0-0 draw at League One side Shrewsbury.
Arsenal fielded a second-string team for the trip to Nottingham Forest, a side who have fallen a long way since they won back-to-back European Cups in 1979 and 1980.
Lichaj headed them in front early on and though Per Mertesacker levelled soon after, Lichaj restored the home side's lead just before half-time.
Brereton extended their lead to 3-1 and after Danny Welbeck had pulled one back with 11 minutes to go, Dowell sealed the win from the spot with five minutes to go on the clock.
Spurs outclass AFC Wimbledon
At Wembley, Spurs were frustrated by an organised AFC Wimbledon team for an hour.
Kane broke the deadlock on 63 minutes, bundling the ball over the line from close range.
The England striker added a second two minutes later with a scuffed left-foot finish from six yards out before Vertonghen finished off the visitors with a deflected third on 71 minutes.
"It was a solid performance from us," Tottenham manager Mauricio Pochettino said.
"The second half was difficult - they started well and had some chances. We scored then and again quick and the game was over.
"We are happy because we're in the draw. We hope to get a home draw. The team deserves this. This is a competition we'll like to go far in."
West Ham draw against Shrewsbury
West Ham goalkeeper Joe Hart admitted his side "got out of jail" by avoiding defeat at Shrewsbury, despite being outplayed by the League One side in their 0-0 draw.
"We were terrible today and Shrewsbury were really good," Hart said.
"It's a tough place to come. We didn't play well. We had three games in a week and there were opportunities for the lads, including myself.
"I can't blame fatigue. There was some terrible football played today and we lost a lot of battles."
Newport shock Leeds
Championship club Leeds United were not so lucky, beaten 2-1 at League Two side Newport County.
Gaetano Berardi gave Leeds an early lead but Newport levelled through a Conor Shaughnessy own goal before Shawn McCoulsky headed the winner late on.
Newport County manager Michael Flynn said his side deserved their win.
"I thought we were the better team in the first half," he told BBC Wales.
"The (Leeds) goal was unfortunate but we had chances and kept going. I told them we don't have to win the game in the first 10 minutes of the second half.
"We got crosses into the box...it was an outstanding header. (McCoulsky) has 11 goals for us this season and he has been superb for us. He was hungry and wanted it and I am delighted."