Spurs led 1-0 at half-time but Aaron Ramsey struck back for the visitors five minutes after the break. Ramsey had another chance after that in Arsenal's best spell but Spurs created all the chances from the 55-minute mark with Gareth Bale twice, Luka Modric, Emmanuel Adebayor and Jermain Defoe and all going close either side of Kyle Walker's spectacular winner.
"We showed another side to our game and that was very pleasing," Parker told the Spurs website.
"In the last three games we've won we've controlled them all and played some great stuff, but this time we had to dig in.
"When they came back to 1-1 they were on top but we managed to go on and win the game. We had other chances as well. In the end 2-1 was a great result, but it could have been more."