Shivajians' captain Juan Barraso was in fine touch on Tuesday, assisting the first goal scored on 30 minutes by Kim Song Yong, and scoring the second himself from the 6-yard penalty spot in the 55th minute.
DSK Shivajians made three changes to the side which faced East Bengal on the weekend. Under-22 players Jerry Lalrinzuala and Rohit Kumar was fielded along with Ongnam Milan Singh.
The visiting team made two notable changes, which saw Shahin Lal Meloli standing under the woodwork and Malsawmfela starting in the forward line. DSK Shivajians settled in well as the match progressed, looking certain to score.
Meanwhile, Chennai were on the backfoot for the first quarter, with little support for Charles De Souza up-front to create any real damage on the break.
The home side got an opportunity to take the lead in the 26th minute when Juan Quero's freekick from the edge of the Chennai City penalty area was parried away by an all-stretched Shahin Meloli. The goal eventually came at the stroke of the half-hour mark.
Juan Quero's free kick found an unmarked Kim Song Yong on 30 minutes, who headed the ball into the net, giving Shivajians the lead. DSK Shivajians doubled their lead, 10 minutes into the second half from the penalty spot.
Juan Quero Barraso, who looked particularly lively at the start of the second-half, found Kim Song Yong with a neat diagonal pass, dissecting the Chennai City FC defence.
In his attempt to cut inside, Song was fouled by Clemente inside the box, leaving the referee with no other option but to flash the yellow card and award DSK Shivajians the penalty.
Quero put the ball past Shahin Lal to give Shivajians a two-goal lead with half an hour to go. As the match entered into the final 20 minutes both teams made a number of changes to impact the game.
Eventually, the hosts bagged maximum points against Chennai City with a two-goal margin to jump to the sixth spot in the league table.