Victory at the Salford City Stadium was the Vikings' third in a row - following surprise triumphs at Warrington and against Hull KR in recent weeks - the first time they have achieved that feat in Super League.
Betts handed centre Declan Hulme his debut for their season finale as Widnes overturned a 4-0 half-time deficit to run in 24 unanswered points in the second half.
Betts said: "It's good to give local lads an opportunity and they did superbly.
"Danny Craven changed the game when he came on and his kicking game gave us good field position.
"Adam Lawton and Jack Owens are also local lads and I've been told it's the first time we have won three in a row in Super League which is good news.
"It was a tough game and Salford did well in the first half.
"It wasn't a free flowing game but we made a great start to the second half.
"The players felt at half-time they weren't far away from getting the field position.
"We are not a top-eight side yet but we are on the journey and not too far away."
While Widnes are guaranteed to finish no lower than 11th, Salford could still finish bottom if London Broncos pull off a shock win at Hull KR on Sunday.
It was an emotional night for Lee Gaskell, Jodie Broughton and Jordan James who were among the Salford players on duty for the last time ahead of the Reds revolution.
But they could not sign off with a win as Brian Noble's men slumped to their fifth defeat in a row despite leading 4-0 at the break thanks to a Mark Sneyd try.
Widnes took charge after the interval to run in two converted touchdowns from Patrick Ah Van and others by Rhys Hanbury and Joe Mellor.
Gareth Hock, one of 12 new signings announced by Salford on Thursday for 2014, made his farewell appearance for Widnes against his future employers - and landed the final conversion to Ah Van's second try in the last minute.
Brian Noble cut a frustrated figure after the match, bemoaning his side picking up injuries over the course of the match.
He said: "We were still in the show at half-time but picked up too many knocks.
"Jodie Broughton did his hamstring and Theo Fages has a bashed hip but we had a huge dig although made too many errors.
"Kevin Brown's kicking game was better than ours in the second half and he put the ball on a sixpence.
"There are exciting times ahead from tomorrow but we owe a big thank you to the 14 or 15 players who are leaving."
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