Spurs bounced back from their FA Cup semi-final defeat last weekend to record back-to-back victories which have put them in pole position for Champions League qualification.
A penalty from Jermain Defoe and Gareth Bale's goal helped them to a 2-1 win over Chelsea, denting the Blues' title ambitions after Manchester United had beaten Manchester City earlier in the day.
Frank Lampard pulled one back late on for Chelsea, but it was a sorry afternoon for Carlo Ancelotti's side, who had John Terry sent off for two bookable offences in the second half.
Dawson could not believe how well his side had recovered from their FA Cup defeat to Portsmouth to beat north London rivals Arsenal and then Chelsea.
He told ESPN: "The lads picked themselves up and put in two fantastic performances.
"The grit, determination and work-rate from the boys was great and the quality came through in the end."
Paul Scholes' winner for United against Manchester City gave Spurs hope of moving into fourth place and they took their chance with style.
Dawson added: "The lads were having their lunch in the players' lounge and when Paul Scholes scored there was a little cheer.
"We have got some more important games to come so it's an exciting time and it'll go right down to the wire."
Spurs boss Harry Redknapp was full of praise for his side, saying: "They've been fantastic. After the disappointment of last Sunday to come back with these two wins is top class.
"We were even better than we were against Arsenal, in the first 30 minutes we completely dominated."
Ancelotti was defiant after the defeat and told ESPN: "The title is still in our hands, we don't have to be afraid, we just have to look to the next game against Stoke.
"I don't think the players were nervous, we knew how important this game was. We didn't do so good but Tottenham played very well, at the same level as they did against Arsenal.
"We were a little bit down, but this is football."
The Italian refused to criticise referee Phil Dowd for sending off Terry, adding: "I don't like to talk about the decisions of the referee, we are disappointed because he (Terry) is not able to play the next game."