Leg-spinner Adil Rashid took 4-11 and pace bowlers Jofra Archer and Mark Wood 4-12 as England dismissed Oman in 13.2 overs.
In reaching their target in 19 balls, England set a record for the fastest chase in a T20 World Cup match and made the ideal response to Saturday’s defeat by Australia in Barbados.
“Even when England won the toss and bowled first, or when Oman were 16-2, I don’t think they would anticipated bowling Oman out for 47,” said Finn, who won 126 caps for England across all formats.
“It just shows the power England have, but it is just one step in the right direction.”
England had to complete their chase inside 33 balls to take their net run-rate above Scotland’s, and Phil Salt hit the first two balls for six.
He was bowled by his third delivery, but captain Buttler finished 24 not out from eight balls alongside Jonny Bairstow, who hit the only two balls he faced for four.
Buttler said the result was “just what was needed” after a washout in their opening game against Scotland and the defeat by Australia.
“It was a really good performance,” he said.
“We have had some really good training sessions and spoke about how we need to stay true to ourselves and trust we have got really good players.
“We spoke about needing to win two games of cricket and, if we had the chance to affect the net run-rate, that would be important.
“We are still in the same position. We still have a must-win game on Saturday.”