The Sri Lankan batsman hit seven fours in his 41-ball knock as Punjab surpassed Kolkata's competitive 153-3 in a last-ball finish at St.
George's Park.
Needing seven from the final over by Kolkata paceman Ajit Agarkar, Jayawardene hit a four while Irfan Pathan (19 not out) fetched the winning runs for Punjab.
The victory helped Punjab climb to the second position in the points table while the struggling Kolkata continued to languish at the bottom with their sixth defeat from eight matches.
The Yuvraj Singh-led Punjab have now won four of their seven matches in this Twenty20 competition.
Punjab were off to a disappointing start with Ishant Sharma claiming Kumar Sangakkara for a duck in the first over but a slew of dropped catches and poor fielding did Kolkata no favours.
Simon Katich (34) was dropped on five by Chris Gayle while debutant Sunny Sohal also thrived on a grassed chance to make a fine 26-ball 25 on debut.
Kolkata's innings was built around Brad Hodge who top