Harry Kane fired Tottenham past third-tier Portsmouth and into the FA Cup fourth round on Saturday as 2021 winners Leicester emerged unscathed from a tricky tie against lowly Gillingham.

Elsewhere on a packed day of third-round action, Southampton came from behind to beat Crystal Palace 2-1 in an all-Premier League tie to give beleaguered manager Nathan Jones something to smile about.

Antonio Conte rang the changes for Spurs for the match against League One Portsmouth but retained a heavyweight forward line including Kane and Son Heung-min.

The in-form Kane broke the deadlock in the 50th minute, receiving the ball on the edge of the box and bending a fine curled effort past the despairing dive of Josh Griffiths.

Kane, with four goals in four matches since missing the penalty against France that led to England's elimination at the World Cup, now has 265 goals for Spurs -- just one behind the club's all-time record scorer, Jimmy Greaves.

Spurs, who have won the FA Cup eight times, were unable to add to their tally but saw out the match fairly comfortably to win 1-0.

"It was a tough game," Kane told the BBC. "We were clear favourites and people probably expected a bigger score but credit to them, they stayed compact and made it difficult."

The 29-year-old said he was trying not to focus on overtaking Greaves.

"I try to not think about it," he said. "Sometimes you can think too much. Obviously I feel in good form and I feel fit. My mindset is to help the team and hopefully the goals will come."

Leicester avoid shock

Leicester manager Brendan Rodgers, who led his side to the trophy two years ago, made multiple changes after his team's third straight Premier League defeat this week.

But he retained veteran forward Jamie Vardy for the match against fourth-tier Gillingham, who are rock bottom of England's Football League.

Vardy was the provider as Kelechi Iheanacho scored the only goal of the game in the 56th minute -- only his second goal of the season.

Leicester squandered chances to double their lead but held out and will now turn their attention to Tuesday's League Cup quarter-final against Newcastle.

Nigerian international forward Iheanacho said it had been tough to break down their opponents in the early stages of the match but hailed an important win.

"This gave us momentum to go to the next cup competition," he said. "We are playing Newcastle. Sort of revenge because they beat us in the Premier League.

"It is not going to be easy but fingers crossed we will go there and fight to our last breath to make sure that we win."

Last year's semi-finalists Palace took the lead against Premier League basement club Southampton through Odsonne Edouard.

But Saints levelled in the 37th minute after some poor defending from the hosts. James Ward-Prowse sent what looked to be an innocuous free-kick into the area but Joel Ward mistimed his effort to head clear.

The ball took a bounce inside the box before evading goalkeeper Vicente Guaita, who moved in the right direction but could not stop it from going into the net.

Southampton took the lead for the first time midway through the second half.

Guaita was attempting to make a routine clearance from outside the area when Adam Armstrong rushed in, stole the ball from the Spaniard and had plenty of time to find the empty net.

Preston came from behind to beat Huddersfield 3-1 while Reading beat Watford 2-0.

Liverpool take on Wolves in the standout match of the day later on Saturday, with Manchester City hosting Chelsea on Sunday.

Manchester United beat Everton 3-1 on Friday in another all-Premier League clash.

Forest Green's tie against Birmingham was postponed on Saturday due to a waterlogged pitch.