Australian David Warner; Steve Smith celebrates with Adam Zampa.
Sri Lanka started the tournament as rank outsiders and finished sixth of the nine teams, registering one of their three wins against the world's top-ranked one-day international side and hosts England.
A throw to the stumps deflected off the bat of a diving Ben Stokes as he tried to complete a second run and raced to the boundary, with Sri Lankan umpire Kumar Dharmasena awarding six.
Sarfaraz Ahmed's side needed to smash the world record for margin of victory in a one-day international but, after winning the toss at Lord's, they failed to muster enough runs to give them a chance.
Bangladesh must be all out for seven or lower if Pakistan are to deny New Zealand a place in the semi-finals alongside Australia, India and England.
The broadcaster said their decision would "ensure as wide an audience as possible is able to watch the game."
England have qualified for the semi-finals and will meet either India or Australia on Thursday July 11. The final is at Lord's on July 14.
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Skipper Dimuth Karunaratne moved from his overnight 49 to score 65 and provided the only bit of resistance in the morning session, which saw 29.3 overs bowled. Boult took two early wickets in one over after Sri Lanka resumed the day at 85 for two. Dhananjaya de Silva on 32 and Dilruwan Perera on five were at the crease.