Chelsea's 2-0 loss at Manchester United allowed Tottenham to trim their lead at the league summit to four point.
Chelsea's 2-0 loss at Manchester United allowed Tottenham to trim their lead at the league summit to four points and Saturday's clash at Wembley was billed as a chance for Spurs to strike a psychological blow.
But Chelsea showed mental resolve to engineer a 4-2 win, Hazard netting the crucial third goal after coming on, and they have the bit between their teeth again prior to Tuesday's visit of Southampton.
"This win maybe gives us more confidence for the rest of the season," Hazard told the Chelsea website.
"We have six games to play in the league and we need to win five if Tottenham win all of theirs, so we will see.
"We lost last weekend against a great team and for the rest of the season, it is always good to have the confidence up.
"Now we play on Tuesday and we need to win to go seven points clear at the top of the league."
Chelsea coach Antonio Conte is unhappy that his side have not been given more time to prepare for Tuesday's game at Stamford Bridge.
But for the first time in over a month, his team have an opportunity to put pressure on Tottenham by playing before them, with Spurs crossing London to face Crystal Palace on Wednesday.
Chelsea face the thorniest game of their run-in on Sunday -- a trip to Everton -- and having slipped to a shock 2-1 loss at home to Palace earlier this month, they will be on high alert against Southampton.
Hazard and Diego Costa are expected to return to Chelsea's starting XI, having started Saturday's game at Wembley on the bench.
Pedro faces a fight to hold onto his jersey after Willian seized the opportunity of a starting berth against Spurs by scoring twice, via a trademark free-kick and a penalty.
Nathan Ake could keep his place in the back three after stepping in to deputise for Gary Cahill, who was admitted to hospital last week with gastroenteritis.
Southampton pulled off a surprise 3-1 victory on their last visit to Stamford Bridge in October 2015, which was their first away win over Chelsea since January 2002.
Four points behind eighth-place West Bromwich Albion, with two games in hand, and a huge 17 points below seventh-place Arsenal, the most Claude Puel's side can hope for is to pip West Brom to eighth.
But midfielder Pierre-Emile Hojbjerg says the calibre of the opposition means they will have no trouble motivating themselves.
"Of course, you say every game is important, but somehow, when you play against number one, it gets a little bit more important," the Denmark international told the club website.
"I saw the game they lost against Manchester United and now they are a little bit under pressure, and we also want to continue getting good results.
"Chelsea away is, of course, maybe the toughest game this year, but I think that we have the possibility to get the result. Why not?
"We are a good team and we have shown it before, so I don't think it is impossible, but it is going to be very tough."
Former Chelsea midfielder Oriol Romeu is back from suspension after missing Southampton's 1-0 win at West Brom and 3-0 home defeat by Manchester City.
Influential centre-back Virgil van Dijk is a long-term absentee with an ankle injury, while striker Charlie Austin is doubtful due to a shoulder problem.