The seamer had Richard Levi and Richard Keogh caught behind by wicketkeeper Ben Cox before Ben Duckett flashed the next delivery to Jack Shantry in the gully.
Chaminda Vaas became the first player in Test matches or ODIs to take three wickets with the opening three deliveries, doing so against Bangladesh in the 2003 World Cup.
The Sri Lanka paceman bowled Hannan Sarkar first up and then took a return catch to dismiss Mohammad Ashraful before Ehsanul Haque poked to Mahela Jayawardene in the slip cordon.