With the dry wicket aiding the spinners, the West Indies' batsmen were simply not scoring and Deandra Dottin was the next player to fall lbw, as skipper Knight added to her half-century with a vital scalp.
Sciver had scored a second century of the tournament against New Zealand, which included a between-the-legs "Nat-meg" shot.
England has won six WWC games in a row - including a 68-run victory over South Africa - following its opening defeat by India.
Bravo could be among a host of key names, including his brother Dwayne and Chris Gayle, to return to the ODI squad to face England.
Knight was eventually bowled by Matthews, having struck five boundaries in her 13th one-day worldwide half-century, with Katherine Brunt adding 14 before Gunn and Marsh helped put on a few late runs to boost England's total.
The lbw calls continued to come, and all-rounder Sciver clinched her third wicket in three overs after Fletcher played all-round her legs.
Despite early aggression from Matthews, who lifted Marsh over long on in her first over, the West Indies soon ground to a standstill against the spinners.
The World T20 champions' luck got no better as opener Matthews was trapped plumb in front by the continuously impressive Alex Hartley for a hard-earned 29. From a run-rate of just over three an over, Windies started to find runs hard to come by as England struck through a combined effort.
Appointments for the 23 July final at Lord's will be made in due course.
"We wanted to put in a really professional performance and there was that carrot of finishing top of the group to stay here in Bristol", Knight told Sky Sports.
Natalie Sciver has smashed two hundreds for England so far, with Beaumont, Taylor and Knight hitting one each, though it was a battling 67 from the skipper that helped the side seal top spot in the group stage courtesy of a 92-run triumph over West Indies on Saturday.
"That character is really nice to see, in this tournament we have found our way out of sticky situations".
"We have seen him during the last Digicel R4Day season show signs of his return to form".
Marsh, so pivotal with the bat, dismissed the unsafe Stafanie Taylor lbw for a 12-ball duck but with DRS available had the West Indian captain reviewed she would have been reprieved with the ball sliding down the leg side. "I'm extremely happy", she said.