There are two more Premier League games to look forward to on New Year's Day, with Tottenham hosting Aston Villa and Chelsea visiting Nottingham Forest.
Spurs may find themselves out of the top four by kick-off, with the Champions League places also coveted by the Blues.
It is a different story for Forest, whose position is looking perilous towards the bottom of the table, while Villa will look to continue their improvement under boss Unai Emery.
Conte must be at a loss to explain his team's ability to make things difficult for themselves.
Their 2-2 draw at Brentford on Boxing Day was the sixth Premier League game in a row in which Spurs have conceded the first goal and 10th in total in 2022/23.
They have lost three of those games to allow Manchester United to close the gap on them in the top four race and may have been overtaken by the Red Devils by the time they run out on Sunday.
Tottenham are 7/4 to finish in the top four and will need to win games like this if they are to record a second straight Champions League finish.
Villa will not make life easy and have clearly improved since Emery stepped into the fold and showed signs of form even when going down 3-1 at home to Liverpool on Boxing Day.
However, Tottenham will still fancy themselves to take the points. There have been goals on both sides in all three of the pair's meetings at the Tottenham Hotspur Stadium and the hosts are in the Result/Both Teams to Score market.
A man who has undoubtedly played his part in games between these sides over recent years is Harry Kane. The England captain responded to his World Cup penalty heartache by scoring in the draw at Brentford and has now netted in his last three Premier League games.
That said, it was Heung-min Son and Dejan Kulusevski who got the goals when the pair last met, a 4-0 Spurs win at Villa Park.
Son is 7/4, while Kulusevski is in the Anytime Goalscorers market and with them stationed either side of Kane, the Spurs' frontline looks irresistible.
A routine 2-0 win over Bournemouth marked a decent resumption to Chelsea's season and they will hope for more of the same against another of last term's promoted sides.
Kai Havertz and Mason Mount both got on the scoresheet but there was bad news for the Blues, as Reece James suffered a recurrence of the knee injury that kept him out of the World Cup.
James will be out for four weeks and Cesar Azpilicueta will likely take his place. In a roundabout way, that could improve Chelsea's defence, especially with Kalidou Koulibaly and Thiago Silva settling in the middle and Marc Cucurella undoubtedly happier in a back four.
Havertz is one of several Chelsea players with a point to prove after the World Cup but looked sharp against the Cherries.
The Germany international is 12/5 to score at any time, and his movement, with his ability to both stretch defences and drop deep, make him dangerous.
Forest again looked a bit ragged in their 3-0 Boxing Day defeat to Manchester United and Havertz could have chances.
Home boss Steve Cooper has commented since that game that he needs to both reinforce his line-up and settle on his preferred team if they are to successfully beat the drop, with the potential that they could be bottom come Sunday at 16:30.
One player who has become vital is local boy Ryan Yates, who has often captained the side this season. However, he does average 2.36 fouls a game and might be a player to look for at in the Player to Be Booked market.