Rutherford smacked seven sixes in his unbeaten 76 off 42 deliveries to provide the bedrock of his team's imposing total of 6-196 in the group C encounter in Mumbai on Wednesday.
Twice champions West Indies then returned to choke their opponents with spin and bundled out England for 166 in 19 overs to top the group with their second successive victory.
England, who struggled even to beat Nepal in their opening group game, once again were unconvincing as they slipped to third, behind Scotland, in their group.
"Disappointing. It's never nice to lose a game, but West Indies played outstanding," England captain Harry Brook said.
"We thought it was a chaseable total for sure but it didn't dew up as much as we expected and didn't skid onto the bat."
Put in to bat, West Indies lost both openers in the first seven deliveries of their innings.
Shimron Hetmyer (23) and Roston Chase (34) steadied the ship before Rutherford walked in to light up the Wankhede Stadium.
He shared a 61-run stand with Jason Holder, who struck four sixes in his 33 off 17 balls, to take West Indies close to 200.
Leg-spinner Adil Rashid excelled for England, conceding only 16 runs in his four overs and claiming the wickets of Chase and Rovman Powell.
England made a flying start before losing Phil Salt (30) in the fourth over.
Chase removed Jos Buttler for 21 and left-arm spinner Motie produced a double strike to turn the heat on England, who slumped to 4-93 at the halfway stage of their innings.
The situation demanded caution and Brook duly curbed his normal aggression but the West Indian spinners would not be denied.
Motie (3-33) caught Brook off his own bowling and Chase trapped Will Jacks lbw to further turn the screw.
Sam Curran, who'd got England out of trouble against Nepal with his death bowling, this time made a valiant 43 not out down the order but lacked support.
"I have put in a lot of work coming into the World Cup," Rutherford said.
"I trust my process and I can score runs in the end when I play with a clear mind. We were maybe 10 runs behind what we wanted given England's powerful batting but the guys bowled well."
