Lloyd White, Danny Craven and Charly Runciman all scored for the Vikings in the first half at the Select Security Stadium after the Broncos had gone in front courtesy of a Mark Ioane try.
Leading 22-6 at the break, Widenes went further ahead through Craven's second try of the game, before Jarrod Sammut pulled it back to 26-10.
However a brace of tries from Joe Mellor on his 150th Widnes appearance took the game away from the visitors to seal the win which moves the Vikings level on eight points with Catalans Dragons.
The two sides will meet in Perpignan next Saturday with the winners securing their Super League status and the losers having to face Leigh Centurions in that Million Pound Game decider on September 30.
Betts is keen to get survival wrapped up in their final Qualifiers game against the Dragons and he claims the Broncos win has put his players in a positive frame of mind.
He said: "We always knew we had to win two games. We are in control. Catalans will feel the same.
"It's a tough ask to go over there and win. We have drawn over there but never won. It's a possible task but we are confident now."