Chhangte, who has played for the India senior team four times, set up Paulinho Dias (46th minute) for Dynamos' first goal before he added his own name to the scoresheet in the 55th minute.
Matias Mirabaje made it 3-0 for the Dynamos in the 66th minute as the Delhi side controlled the game for most part of the opening.
Emiliano Alfaro pulled one back for Pune in the 67th minute as the Balewadi Stadium saw four goals in the space 21 minutes after a barren and uneventful first half.
Marcos Tebar further reduced the margin for Pune with a goal in the last minute of stoppage time (90+5) but it was too late in the match as the referee blew the final whistle just after the ball hit the net.
The 20-year-old Mizoram player Chhangte was the star of the night with a goal and an assist. As soon as the second half started, he sent a measured cross into the Pune box from the left after a neat passing with Sena Ralte.
Captain Kalu Uche and Paulinho went for the header. Eventually it was Paulinho who found himself at the end of the cross as he headed the ball into the net.
The goal suddenly injected life into the match and the Dynamos doubled the lead eight minutes later. Pune defender Gurtej Singh failed to hold on to a backpass and Chhangte pounced on the chance and then lobbed the ball past an onrushing goalkeeper Kamaljit Singh.
Uruguayan Mirabaje then took the match out of Pune's reach in the 66th minute as his left footed shot off a cross from Pritam Kotal beat Kamaljit and found the back of the net.
Alfaro immediately reduced the margin for Pune in the next minute as he turned inside the Dynamos box and sent a low left footer that beat goalkeeper Albino Gomes after a slight deflection from a defender.
Tebar scored another goal for Pune from the last kick of the match, connecting a low cross from the right by Marcelo Pereira who was the highest scorer last season while appearing for Dynamos.
With the win, the Dynamos continued their stranglehold over Pune in the ISL. The Delhi side have now won four times in seven meeting. Pune have won only once while two matches have been drawn affairs.