Costa Rican Bryan Ruiz opened the scoring midway through the first half, seconds after Csaba Feher had been sent off for a two-legged tackle on Theo Janssen.
Twente sealed their first title 16 minutes before time when Miroslav Stoch came in from the right to double the lead.
"This was a fantastic afternoon and (it was) amazing how my players handled the enormous pressure," former England coach McClaren told Eredivisie Live TV.
"The boys did so well today, though they should have scored more, in my opinion, to seal the win earlier but they have been doing this the whole season.
"Last season we lost the cup final (and) finished second in the league but we kept growing and growing and today it proved that we are more experienced after all our big games also in the Europa league."
Twente finished with 86 points after 34 matches, one point above Ajax Amsterdam who won 4-1 at NEC Nijmegen on Sunday.
Ajax, who could have taken their 30th title if Twente had failed to beat Breda, settled the match in Nijmegen before the interval with Luis Suarez, Demy de Zeeuw and Marko Pantelic on target.
Suarez scored his 35th goal of the season in the second half to become the league's top scorer before Saidi Ntibazonkiza earned Nijmegen their consolation goal.
AZ Alkmaar and PSV Eindhoven shared the points in a 1-1 draw, with Otman Bakkal opening the scoring after 61 minutes for PSV and Mounir El Hamdaoui equalising eight minutes later.
PSV finished third with 78 points, while Alkmaar slipped to fifth with 62 after being leapfrogged by Feyenoord who thrashed Heerenveen 6-2, with Roy Makaay scoring a hat trick in his final league appearance.
