The entire morning session was wiped out by persistent, heavy showers in Manchester, halting the home side's charge after they dominated with bat and ball on Sunday.
Having set the Windies a notional target of 399, Broad reduced them to 10 for two with his seventh and eighth wickets of the match.
That took the 34-year-old seamer to 499 career scalps and it is now a question of when, not if, he joins team-mate James Anderson in the exclusive 500 club.
Only six bowlers in history have achieved that mark, with Anderson, Glenn McGrath and Courtney Walsh the only pacemen.
The bad weather has played into the West Indies' hands, with a draw enough to see them retain the Wisden Trophy, but with 98 overs possible on day five England will still hope to have enough time to seal a 2-1 win.