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.
Vitaliy Mykolenko's 39th-minute own goal had put Luton ahead before Jack Harrison cheered the Everton faithful with an equaliser in the 55th minute, hammering in a low shot that Luton keeper Tim Krul allowed to let slip through his hands.
City midfielder Phil Foden was not named in England coach Thomas Tuchel's squad for a pair of upcoming games, after requesting to be omitted. Foden said this week he was nursing an ankle injury.
Manchester United were given an early scare at Newcastle United on Wednesday before hitting back for a 2-1 victory that restored their seven-point cushion at the top of the English Premier League. Fourth-placed Aston Villa's Champions League ambitions were dealt a blow with a 2-0 loss at Manchester City while Stoke City climbed out of the bottom three with a 2-0 home victory over Bolton Wanderers. West Ham United won 1-0 at Wigan Athletic.
IMAGES from the Premier League matches played on Wednesday.
Liverpool substitute Curtis Jones and Everton midfielder Abdoulaye Doucoure were also shown red cards after the game, and the final whistle sparked a scuffle between both sets of players.
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.
Manchester United opened up a seven-point lead at the top of the Premier League even as rivals Man City suffered a shocking reverse at Sunderland on the Boxing Day.
And champions Arsenal face Blackburn Rovers in next month's FA Cup semi-finals in Cardiff.
The Premier League leaders were held to a 2-2 draw.
'If you were to lift the two trophies, I think you have a pretty good chance to be on a nice list of captains that have achieved great things in this club.'
Manchester United's title charge was slowed when they drew 0-0 at Newcastle United on Tuesday and missed the chance to move nine points clear of Arsenal at the top of the Premier League standings.
Manchester United's 100 per cent start to the Premier League season ended when they were held to a goalless draw against Newcastle United at Old Trafford on Saturday.
It is the 16th Premier League game to be postponed due to COVID-19 cases and injuries this month.
After a dreadful start to the season, Mikel Arteta's Arsenal are now up to 10th place in the Premier League and they never looked in danger against a Newcastle side that looks demoralised.
Equality and inclusion group Kick It Out are reportedly planning to offer education workshops in Newcastle to supporters to explain how impersonating Arabs could be considered be racist or culturally insensitive.
IMAGES from the Premier League matches played on Saturday.
Newcastle United have signed French winger Gabriel Obertan on a five-year deal from Premier League champions Manchester United, the north-east club said on their website on Tuesday.
Images from the Premier League match between Nottingham Forest and Crystal Palace at Selhurst Park, London, on Monday.
Manchester City's spending of more than 180 million pounds ($223.58 million) was the second-biggest outlay ever worldwide by a club in the January transfer window.
Liverpool continued their march towards the Premier League title with a 1-0 victory over Everton in a scrappy Merseyside derby as Diogo Jota slotted home the winner in the second half on Wednesday.
Holders Manchester City will take on RB Leipzig, Red Star Belgrade and Young Boys in Group G.
Chelsea beat London rivals Tottenham Hotspur 1-0 on Thursday thanks to a goal by Argentina's Enzo Fernandez
Manchester United crushed Newcastle United's hopes of a claiming a first domestic trophy for nearly 70 years with a clinical 2-0 victory in the League Cup final at Wembley on Sunday.
Wolverhampton Wanderers shared the spoils for the sixth time in 10 Premier League games as Jonny Otto equalised in the second half to earn them a 1-1 draw at Newcastle United on Sunday.
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.
IMAGES from the Premier League matches played on Sunday
A makeshift United defence that included Casemiro at centre-back was easily picked apart by Palace on several occasions
West Ham beat Premier League strugglers Leicester City 2-0 at the London Stadium on Thursday thanks to an early strike from Tomas Soucek on his 30th birthday and an own goal just before halftime.
The decision follows a legal challenge by Manchester City against the league's Associated Party Transaction (APT) rules, which regulate commercial deals between clubs and companies linked to their owners if considered above fair market value.
Alexander Isak's early headed goal lifted Newcastle to a 1-0 victory over Arsenal on Saturday at St. James' Park, as Eddie Howe's men delivered a blow to Arsenal's title chase with their first win in six Premier League outings.
England debutant Myles Lewis-Skelly got new coach Thomas Tuchel's reign up and running as the 18-year-old scored the first goal in a 2-0 home victory against Albania in their World Cup qualifying Group K opener on Friday.
Manchester City gave Kevin De Bruyne a victory in his final appearance at Etihad Stadium, as Omar Marmoush scored a stunner in a 3-1 Premier League win over Bournemouth on Tuesday that saw them climb to third in the table.
Chelsea won for the first time in six Premier League matches when they beat relegation-threatened Wolverhampton Wanderers 3-1 at home on Monday.
Manchester United dropped out of the Premier League's top four
IMAGES from the English Premier League matches played on Saturday.
A summary of Saturday's action in the FA Cup.
Manchester City and Arsenal closed in on Premier League leaders Liverpool with contrasting victories on Saturday as Manchester United's bubble was burst by Fulham.
Manchester United fielded a defence boasting only two first-team appearances but still proved too good for Premier League rivals Newcastle United with a 2-1 win in the League Cup third round at Old Trafford on Wednesday.