The Whites put four past the Clarets without reply at Turf Moor to strengthen their hopes of a top half finish.
Mateusz Klich opened the scoring, with Jack Harrison doubling the advantage partway through the second half and Rodrigo adding a brace late on.
Speaking after the game, Marcelo Bielsa was quick to praise his record signing too.
He said: "Rodrigo is a player at a very high level.
"He's one of the strikers for the Spanish national team and they are a powerhouse. He's a player, like I've said before, that it takes him a while to get to his full form. When he finally finds his full form he's a player that is very unbalancing.
"The players have legitimate aspirations to play more but the best thing for any player is to be in conditions to play well," he said.
"Then you can play well or not well. If you're not in good form, it's very difficult to play well. I think these 50 minutes that Rodrigo played against Tottenham and today, that were at a very good level, are preferable than to play a lot of minutes when you're not at your best. I think in the game against Tottenham and the game today, I think we saw a version of Rodrigo close to what he's capable of."
We’ve gathered the best of today’s Premier League transfer speculation below...