Mink van der Weerden's successful penalty corner conversion in the 53rd minute turned out to be the winner after Delhi's Tristian White's 39th-minute field goal cancelled out Robert van der Horst's 15th-minute strike.
With this win, Punjab took their points tally to 11 points and leapfrogged Uttar Pradesh Wizards, who have eight points from three matches, while Delhi, with five points from four matches, remained in the sixth and final spot.
Dabang Mumbai are on top of the table with 23 points from seven matches, while Kalinga Lancers are second with 20 points from seven matches. Third-placed Ranchi Rays have 17 points from seven games.
The match between Punjab and Delhi saw the latter, with their brand of Indo-Australian style of attacking hockey, starting on a strong note, penetrating Delhi circle regularly.
Early into the game, Satbir Singh couldn't connect a base-line left cross from debutant Mirco Pruyser at the right post as the ball just bounced awkwardly, in a big relief to the home camp.
But Punjab kept their tempo and found the deserving lead in the 15th minute when Satbir snatched the ball from Manuel Brunet at the left of the halfway line before squaring pass to van der Horst. The veteran Dutch star then employed a ripping back-hander from the edge of the circle to beat goalkeeper Vincent Vanasch.
After the goal, Delhi sat back and when Punjab slightly dropped their energy towards the end of the second quarter, the hosts gathered some steam.
Delhi got two quick penalty corners but Rupinder Pal Singh and Justin Reid-Ross' flicks were not strong enough to beat Punjab goalkeeper Tristian Clemons.
Delhi continued the way they ended the second quarter, with pace and momentum. Mandeep Singh found a great opportunity to level the scores following a quick counter-attack. With two defenders chasing him, his drive went inches away from the right post.
The equaliser then came in the 39th minute when White's clinical drive from the right beat Clemons' stretched left foot at the near post.
Couple of minutes later, Clemons swiftly stuck out his right hand to deny a back-hander from Mandeep.
Delhi continued to pile pressure on Barry Dancer-coached Punjab, who conceded a penalty corner in the 47th minute. But Rupinder's flick was out of the mark.
Punjab slowly broke free from the spell of pressure and earned a penalty corner in the 53rd minute when Pruyser's hit bounced off after being defended. This allowed his compatriot, set-piece specialist van der Weerden to come into play and the latter fired a grounder to the right corner to make it 3-2.
This proved to be the winner for Punjab, as Delhi wasted many chances, including a penalty corner, towards the end.