Green, who became the IPL's most expensive overseas recruit when Kolkata paid $2.77 million for his services, played their first three matches of the season solely as a batter while completing his recovery from a lower back injury.
After contributing an unbeaten 32 in Kolkata's 181-4 against Lucknow Super Giants, the sight of Green loosening up drew cheers from a sparse Eden Gardens crowd.
Handed the ball in the ninth over, he removed Lucknow captain Rishabh Pant with his second delivery, but the over cost 12 and he was taken out of the attack.
The 26-year-old returned for the penultimate over with Lucknow needing 30 off 12 balls but was milked for 16 by Mukul Choudhary, who finished 54 not out off 27 balls.
Lucknow sealed victory with the last ball, leaving two-time champions Kolkata without a win after four matches. Their only point came from a washout against Punjab Kings.
Kolkata batter Rovman Powell remained optimistic.
"If you look at IPL history, teams that win are the ones that peak in the middle and later stages," the West Indian told reporters after their loss by three wickets.
"It's not easy when you don't start well, but our destiny is still in our hands. We still have games left.
"If we keep putting in the work, the results will come. Sometimes it's not just about the result - tonight was a good game, we just ended up on the wrong side. But wins will come if we keep doing the right things."
Kolkata are ninth in the 10-team IPL, above Chennai Super Kings on net run rate.