Knight's side had already secured a place in the semi-finals following victory over New Zealand on Wednesday, while West Indies had been eliminated on the back of four defeats.
But Matthews was hit in front to Hartley and lbw in the 24 over and Deandra Dottin (7) missed a sweep at off-spinner Heather Knight and was also lbw 20 balls later at 73 for four in the 27th over. Sciver has two hundreds.
England will now face South Africa in the semi-final on July 18 in Bristol.
Tammy Beaumont made a resolute 42 as she helped rebuild the England innings alongside Knight.
Earlier, England opener Lauren Winfield could only manage 11 before she went in the 10th over, caught at deep square leg to give 16-year-old left-arm seamer Qiana Joseph a first one-day global wicket.
In the next over, Sarah Taylor edged a sharp catch to Matthews at slip off medium pacer Deandra Dottin, to depart without scoring at 54 for two in the 11 over.
Sent in to bat, England were restricted to 220 for seven against the bowling of Afy Fletcher three for 33.More news: IBM claims breakthrough in mainframe encryption
That stand paved the way for a 68-run win, although South Africa put in a valiant effort as they became the first side to score over 300 batting second in a Women's ODI.
In reply, West Indies soon found themselves two wickets down in the 13th over with less than 40 on the board after opener Kycia Knight was run out for 17 and Taylor trapped leg-before by Marsh.
Sciver's first real contribution with the ball then came in Saturday's rout of West Indies, which secured a last-four clash with South Africa on Tuesday, as she returned remarkable figures of three for three from four overs.
Sciver's four-over spell ended with three wickets for just three runs, and one maiden.
Beaumont said: "We fielded and bowled well and won by 92 runs in the end so it's good for us".
On the other hand, back from a 59-run loss to Australia, the South African skipper believed taht the pressure is on the hosts to proceed to the final.
A campaign which started with so much promise went badly awry when the Caribbean side lost their first four games to see their hopes of reaching the semi-finals dashed.