The North London club fought off a late siege by the Capital One Cup winners to hold onto a 2-1 win that keeps Andre Villas-Boas' side four points clear of fifth-place Arsenal.
Andre Villas-Boas' side fought off a late comeback from the Swans in their 2-1 victory at the Liberty Stadium that keeps Spurs in third place, and Parker was pleased to "grind out" the result.
"Swansea put us under pressure the longer the game went on," Parker told the club's official website. "They are a very good team and we had to show a different side to our character at the end. We did that to grind out the result.
"It's a massive win for us. Before the game started, winning was always going to be the most important thing and we managed to come away with the three points.
"That was crucial after a couple of defeats in the league. We've stopped the rot, picked up a big win and now we move on again."
Spurs remain in third place, two points clear of Chelsea and four clear of Arsenal, but both of their London rivals hold a game in hand.
Villas-Boas' side faces Chelsea at Stamford Bridge on April 13, before champions Manchester City visit White Hart Lane the following week in a challenging stretch.