Two first-half goals in nine minutes from Aaron Ramsey and Neil Taylor set Wales on their way before Bale wrapped up victory after the break.
Wales blew away Russia with an irresistible display to reach the last 16 as they showed their nerve and class in Toulouse.
Chris Coleman‘s men were already heroes back home after reaching their first major finals since 1958.
But the entire nation will be falling in love with them at this rate after a dazzling display which will leave fans dreaming how far they can go.
Wales needed a win in their final Group B game to be sure of reaching the knock-out stages.
But despite the tense stakes, they produced their best performance yet in France to dump out sorry Russia, who were a shambles.
Man of the match Aaron Ramsey got Wales off to a flying start in the 11 minute after his fine finish capped a slick breakaway.
Then left-back Neil Taylor netted his first international goal ever in the 20 minute as Wales courageously piled forwarded.
Taylor getting on the score-sheet suggested it was going to be a memorable night for the Welsh, who dominated the 33,000-capacity Stadium de Toulouse.