England Women scored 161-5 in their 17 overs, thanks to a brilliant innings from Alice Capsey, who scored 51 off 27 balls.
Sri Lanka Women were then reduced to 55-3 in the 6 overs due to some excellent bowling by Charlie Dean and Manika Gaur.
The rain-affected game had so many breaks, with England Women winning by 12 runs (DLS).
Alice Capsey was named the player of the match for her innings of 51. She was also the leading run-scorer for England, with 51 runs.
Mahika Gaur earned her debut wicket for England in T20Is, dismissing Sri Lanka captain Chamari Athapaththu.
Sri Lanka Women fought hard but were ultimately unable to chase down the target. They will look to bounce back in the second T20I, which will be played on Saturday.