The hosts struck through two second-half goals from Lallianzuala Chhangte (55') and Adria Carmona (58') while Sergio Cidoncha (39th) and Tiri (77') got on the scoresheet for the visitors who climbed above NorthEast United FC at the top of the table on goal difference.
Delhi remain rooted to the eighth position with four points from seven games.
The teams started in cagey fashion with neither of them able being to assert their dominance over the ball. It were the visitors who carved the first real chance of the match with Tiri's header from a Cidoncha corner flying straight into the hands of Delhi custodian Francisco Dorronsoro.
Another Cidoncha set-piece threatened Delhi's goal again. The Spaniard's floated free-kick found Tiri unmarked at the edge of the box with the defender redirecting the ball towards the danger area. However, the hosts' defence was alert enough this time to clear the danger.
The game failed to really liven up as the first period progressed with chances coming at a premium for both teams.
The visitors, however, broke the deadlock in the 39th minute following a quick breakaway from a Delhi set piece.
Rene Mihelic's free-kick at the other end was cleared towards Gaurav Mukhi who surged forward towards an outnumbered Delhi defence before laying the ball for Cidoncha who applied the finishing touch.
Desperate for an equaliser, Delhi coach Josep Gombau made all three changes at the interval with Andrija Kaluderovic and Adria Carmona coming on. And the hosts were level within 10 minutes into the second half after a dreadful error from Robin Gurung.
The Jamshedpur defender's poor back pass was duly intercepted by a surging Chhangte who made no mistake after skipping past Subrata Paul.
Just minutes later, the hosts were in front with Chhangte providing the assist for the goal this time. The Delhi winger's cross found its way to an unmarked Carmona at the far post and the substitute gleefully converted to make it 2-1.
The hosts were unable to hold on to their lead for too long though with Jamshedpur equalising through a corner kick. Carlos Calvo's corner kick was inadvertently flicked on by Marcos Tebar towards the path of Tiri at the far post who guided the ball into an empty net.
The teams pressed for a late winner with substitutes Tim Cahill and Kaluderovic coming close with headers at both ends. However, there would be no more goals with the hosts left wondering what might have been once again.
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