The Arsenal midfielder claimed that his team-mate is "up there with the best" but described his influence in midfield as different to that of former captain Cesc Fabregas
Wilshere jokingly suggested that the Spaniard's nickname "should be Messi" and described his influence as different to that of former captain Cesc Fabregas, who was similarly integral during his time at the Emirates.
Cazorla scored Arsenal's fourth goal after setting up Olivier Giroud to put the hosts 3-1 up on the stroke of half-time.
"He was different class,'' Wilshere told reporters. "He is a dream to play with. He never gives the ball away. There was one point when there were three players around him and he just dribbled out of it. That is up there with the best.
"I'll have to watch it again to learn a few things off him. He is a different player to Cesc. Cesc is more of a passer. With Santi he can pick the ball up, beat people. He has a great shot."
Cazorla was the victim of a tackle that earned Emmanuel Adebayor, who had given Tottenham an early lead, a red card in the first half and Wilshere felt that the Togo striker could have no complaints about referee Howard Webb's decision.
"It was a high tackle,'' Wilshere commented. "It was pointless really. He didn't have to do it because it was in his own half. It was a turning point in the game."
Another key contributor in the victory was Theo Walcott, who is yet to agree a contract extension with Arsenal ahead of the expiry of his current terms next summer.
"I hope he signs - he's great to have around,'' Wilshere said. "We all know what Theo brings to the team. He has got pace, he can go behind and his movement and timing of the runs is probably the best around.
"So he can play anywhere up front, right, left, central. He wants to play down the middle, so I think he will get his chance - he will just have to be patient."
Wilshere explained that Tottenham posed a different, more physical test under Andre Villas-Boas following the sale of playmakers such as Luka Modric and Rafael van der Vaart in the summer transfer window.
"Last year they had Modric, Van der Vaart and [Scott] Parker down the middle," Wilshere added. "They are more physical this season than last, when they were more creative. It is still a good team and a threat for the fourth position.
"It was massive, for the fans as well, to get the momentum going before Wednesday [when Arsenal play Montpellier in the Champions League]. We need to win."