The hosts had plenty of chances to kill the game as a contest particularly after they had restored parity.
Chennaiyin have not had the best of starts and are now placed fifth with nine points from six matches.
Dynamos lost their first match of the tournament away against FC Goa 0-2 while Chennaiyin were beaten 2-3 at home by title holders Atletico de Kolkata.
Delhi began their campaign with a 0-2 loss against FC Goa on 4 October despite controlling the match in patches and having come close to scoring on a few times.
Postiga struck once in each half, while Frenchman Valmiro Lopes Rocha (Valdo) was the other scorer for the winners at the packed Jawaharlal Nehru Stadium.
Chennaiyin’s build-up to the ISL has been better than last year and Materazzi was happy with the preparations.
ISL side Chennaiyin FC on Tuesday announced the signing of Brazilian duo Raphael Augusto and Mailson Alves Barreiro Veriato for the upcoming tournament
Former Brazil international midfielder Elano will rejoin Chennaiyin FC on loan for the 2015 Indian Super League season, the club said.