The Blues made the breakthrough just before half time when captain John Terry fired in from close range after Spurs failed to clear their lines from a free kick.
Here, Sports Mole takes a closer look at the action between the two teams on a successful day for Chelsea.
On target: 3
On target: 2
Was the result fair?
Spurs will be disappointed that they did not make their dominance count in the first half, but the fact is that Chelsea were more clinical in front of goal and ultimately ran out deserved winners thanks to a solid all-round display.
Chelsea were second best for much of the first half as Spurs showed more desire and invention going forward. A number of the Blues' key players - Cesc Fabregas and Eden Hazard in particular - struggled to make an impact on the game. Despite these shortcomings, they gave themselves a huge boost at the end of the half when John Terry scored to put them in front.
When the sides came back out after the break, Chelsea looked more like the team that has imposed itself on the Premier League this season. They were more physical than Tottenham, dominated the key areas and landed a killer blow when Costa doubled their lead. From that moment on, Mourinho's men looked in control and saw out the match in a professional manner.
Spurs looked good during the opening 45 minutes as they showed no fear in getting on the front foot and attacking Chelsea. Despite an encouraging display, they were made to pay for some poor finishing when they went 0-1 behind on the stroke of half time. Terry's goal clearly rattled Mauricio Pochettino's men because they were far more nervy and unsure of themselves in the second period.
Players such as Harry Kane and Christian Eriksen only came to life in fits and starts, while their defenders struggled with the physicality of Costa. Pochettino himself will be aware that his team found it hard to shake off their recent malaise in the Premier League and Europa League, though they can be proud of their efforts against dogged opposition.
Sports Mole's man of the match
John Terry: Chelsea's captain led by example at the back and proved just how important he is to the team by scoring their opener. When Spurs piled on the pressure in the first half and at the end of the game, Terry was there to keep his side organised and focused.
More of a collective error than an individual one, Spurs should have done much better in clearing the ball in the build-up to Chelsea's opening goal. Instead the ball pinged around the box before Terry fired in with little pressure on him.
Anthony Taylor did a good job of allowing the game to flow in the first half, but he was forced to put his foot down after the break as more and more petty fouls were being committed by both sets of players. However, this was a solid display from the official on what could have been a tricky game to run.
Chelsea: The Blues continue their pursuit of the Premier League title on Wednesday when they travel to West Ham United.
Tottenham: Spurs are back in action on Wednesday with the visit of Swansea City to White Hart Lane in the Premier League.