Ange Postecoglou ultimately paid the price for an horrendous English Premier League season which saw Tottenham finish 17th.
Nuno Espirito Santo's side took the lead after five minutes when a corner fell to Elliot Anderson on the edge of the area and his powerful deflected drive found the net.
Forward Rasmus Hojlund scored twice to allow Manchester United to come back from a goal down and get a 2-1 win at six-times Czech champions Viktoria Plzen in the Europa League on Thursday.
Images from Saturday's action in the Premier League.
Reach fifth round for first time in 10 years
Tottenham Hotspur's Brennan Johnson, Dejan Kulusevski and Dominic Solanke got on the scoresheet in a 3-0 victory over 10-man Manchester United in the Premier League on Sunday as the visitors ran roughshod over the bedraggled Old Trafford side.
Arsenal emerged victorious over Tottenham Hotspur at their rivals' home ground. Gabriel Magalhaes' decisive header in the second half proved to be the difference-maker
Postecoglou moves a step closer to making good on his reputation for securing silverware in his second season at clubs and delivering a first cup for Spurs since they won the League Cup in 2008.
IMAGES from the Premier League matches played on Sunday
Joshua Zirkzee scored the winning penalty for 10-man Manchester United against Arsenal after their hectic FA Cup third round tie finished 1-1 after extra time.
Lazio, who had won all four previous games, were held to a frustrating scoreless draw by a Bulgarian side who came to defend.
Arsenal were held to a 1-1 Premier League draw by London rivals Fulham on a grey wet Sunday at Craven Cottage as Raul Jimenez scored early for the hosts and William Saliba equalised for the visitors at the start of the second half.
Marcus Rashford and Joshua Zirkzee bagged two goals apiece as Manchester United thumped Everton 4-0 on Sunday in new manager Ruben Amorim's first Premier League match at Old Trafford.
Moises Caicedo's blistering second-half strike cancelled out a Bruno Fernandes penalty as Chelsea salvaged a 1-1 draw with Manchester United on Sunday.
Images from the English Premier League matches played on Sunday night.
Images from Sunday's action in the Premier League.
Manchester City have now won only once in 11 games in all competitions.
Eriksen sends message of support to Lockyer following cardiac arrest
A brilliantly-worked goal by Ryan Christie and a Justin Kluivert penalty gave Bournemouth shock 2-0 Premier League win at home to 10-man Arsenal.
Championship (second tier) side Rotherham, who haven't made it through to the fourth round of the competition since 2001-02, kept their composure early on as Fulham controlled the play.
Manchester United's Alejandro Garnacho scored with a magical overhead kick in the third minute to send the visitors on their way to a 3-0 victory over an Everton team already reeling in their first Premier League game after being docked 10 points.
Manchester City won an unprecedented fourth straight English top flight title with a 3-1 win over West Ham United.
Tottenham Hotspur beat Nottingham Forest 2-0 away with goals by Richarlison and Dejan Kulusevski for a second straight win that nudged them closer to the Premier League top four on Friday although they had midfielder Yves Bissouma sent off late on.
Tottenham Hotspur hammered 10-man Aston Villa 4-0 in the Premier League on Sunday thanks to four second-half goals, allowing them to close the gap with their Birmingham rivals to two points in the chase for Champions League football next season.
Arsenal had more than twice as many chances but failed to take any as the visitors defended gamely.
Images from the English Premier League matches played on Saturday night.
Wolverhampton Wanderers stunned Tottenham Hotspur 2-1 with stoppage-time goals from Pablo Sarabia and Mario Lemina on Saturday, thwarting the visitors in their bid to reclaim top spot in the Premier League table.
Liverpool snatched three points with a wild 1-0 victory over relegation-threatened Nottingham Forest.
Bukayo Saka scored either side of halftime as Arsenal crushed second-bottom Burnley 5-0.
Following captain Sergio Busquets' positive test at the weekend, Spain's players have been in isolation and only able to train on an individual basis - with their first game just three days later.
Images from the English Premier League matches played on Sunday night.
Images from the English Premier League matches played on Saturday.
AC Milan entered the Champions League quarterfinals for the first time in eleven years, with a draw in the round of 16 second leg against Tottenham Hotspurs.
Ibrahimovic and Lukaku, who played together at Manchester United, exchanged words at the end of the first half before the pair had to be restrained as the players left the pitch for the interval.
Southampton clinched a thrilling comeback draw against Tottenham Hotspurs in their Premier League encounter on Saturday.
Kane's diving header made it 2-0 in the 37th minute to send Tottenham's fans into delirium.
IMAGES from the Premier League matches played on Saturday
Winger Emil Forsberg scored a double, including the second fastest strike in European Championship history, before Viktor Claesson's stoppage-time goal to help Sweden seal a 3-2 win over Poland on Wednesday and top Group E, heading into the last-16.
Images from the English Premier League matches played on Sunday
Manchester City's bid to chop Arsenal's Premier League lead to two points was scuppered as Harry Kane's record-breaking goal earned Tottenham Hotspur a 1-0 win.