Yeovil, who went into the game after successive draws, welcomed back goalkeeper Marek Stech following a four-month lay-off after he broke two bones in his hand against Birmingham City in August.
And Stech was busy early on as Blackburn piled on the pressure, with Cairney, Dunn and Rhodes all going close.
Yeovil were much improved in the second half, with Miller's powerful shot hitting the crossbar.
But, Rovers made Yeovil pay for some slack defending shortly before the hour mark when Dunn fed Rhodes, who clinically finished into the top corner.
Undeterred by the setback, Yeovil continued to threaten and came inches away from an equaliser minutes later when Ralls saw his curling effort crash off the post.
Yeovil manager Gary Johnson:
"It's a disappointing result but we mustn't be devastated about it.
"We didn't get our passing game going in the first half and kept giving the ball away. If you do that against a top team in this division then you'll be in trouble.
"In the second half we kept the ball better, created a number of chances and hit the bar and the post. We were in the ascendancy, but then their goal came on the break against the run of play."
Blackburn manager Gary Bowyer:
"Jordan is a top lad, his manners are unbelievable, he's polite and popular at the training ground.
"His work rate is phenomenal, he never moans or gets carried away and all he's bothered about is his next goal - it's a fantastic attitude to have.
"You saw today there's more than one player who will attract Premier League interest. I've got no problem with that as all of our players should want to play at the highest level. It's not just Jordan, we have a number of very good players."
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