Strikes by Aaron Ramsey, Neil Taylor and Bale sent the Welsh on their way to the landmark win for a side appearing in their first major tournament since the 1958 World Cup.
England’s scoreless draw with Slovakia meant Roy Hodgson’s men dropped to second in Group B. Wales could not believe their luck.
“To finish top is a bonus for us,” said Bale.
The Real Madrid forward was a constant threat in Toulouse. He grabbed his third goal of the tournament by cleverly dinking the ball past Igor Akinfeev with the outside of his right boot in the second half.
Bale is now the tournament’s top scorer and the first player to score in all three group games since Milan Baros hit three for the Czech Republic in 2004.
“The performance was probably the best I’ve been involved in,” said Bale.
“We always said ‘have no regrets’. What support and what an amazing way (to go through).
“We started very well, we didn’t feel too nervous at the start and were very confident.
“To top the group, it is a dream for all of us, we said we didn’t want to just make up the numbers and we can’t do more than we have.”
Wales’ next fixture will be in Paris on Saturday. They will not find out their opponents until the final round of games in groups A, C and D.
Coach Chris Coleman knows he must now manage expectations.
“We never look past the next game, because we can’t afford to do that. We have to take it challenge by challenge,” said Coleman.
“This is new for us, it’s exciting. But three games ago we lost 3-0 against Sweden, so I don’t have to remind the players.
“Football can change really quickly. Once you think you’ve arrived … you’ve never arrived in football.”
Regularly described as a one-man team built on Bale, the Welsh collective display was impressive.
Arsenal striker Aaron Ramsey, Joe Allen, Bale and Sam Vokes were the key men in the offensive performance that overwhelmed the Russians from the early stages.
Ramsey gave Wales an 11th minute lead when he ran on to Joe Allen’s superb delivery down the middle to push the ball past the onrushing Igor Akinfeev.
Nine minutes later Taylor ended a six-year wait to score a competitive goal when he ran on to Bale’s deflected delivery to beat Akinfeev at the second attempt.
“In my wildest dreams, I never thought Taylor was going to get one of the goals, but he deserves it,” said Coleman.
At their last major tournament, Wales made it to the 1958 World Cup quarter-final against Brazil but without their big star, Juventus striker John Charles.
The match was notable for Pele’s maiden international goal in Brazil’s 1-0 win.
Asked what this feat means for them, Ramsey said: “We’ve been waiting for this competition, to be in the finals for a long long time now and we’re finally here.