Denly opened the bowling and removed both Sri Lanka openers Niroshan Dickwella and Kusal Mendis.
Adil Rashid claimed 3-11 to stifle the hosts before Denly returned with two wickets in the final over as Sri Lanka were bowled out for 157 off 20 overs.
Jason Roy hit an eventful 69 off 36 balls as England posted 187 for 8.