The trio replaced Kasun Rajitha, Bhanuka Rajapasa and Oshada Fernando, while opener Danushka Gunathilaka remained unavailable due to injury.
Perera last played a T20I nearly a year ago, since when he has battled poor form. He appeared to have put that behind him during the ODIs against West Indies, where he has contributed to a pair of Sri Lankan wins with 68 runs off 47 balls across the two games.
Pradeep, who had missed the series against India last year due to injury, returns to claim his spot at the expense of Rajitha, who had replaced Pradeep for that India series. Allrounder Jayasuriya had last played an international in November last year.
The 15-man squad will be captained by veteran fast bowler Lasith Malinga. Sri Lanka are currently engaged in a three-match ODI series against West Indies, which they have already won with a game to spare. The final ODI will take place on 1 March, followed by the two T20Is.