The Whites took the lead thanks to a Mateusz Klich strike, and doubled their advantage courtesy of an effort from Jack Harrison just before the hour mark.
Record signing Rodrigo then wrapped up the points late on with a quickfire double, and manager Marcelo Bielsa was eager to praise the Spain international after the match.
Speaking to the press, 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...
1. Brighton told to sign Toney
Former Crystal Palace striker Clinton Morrison has claimed Brighton should sign Brentford hitman Ivan Toney to push them on to the next level. (Sky Sports) (Photo by Justin Setterfield/Getty Images) Photo: Justin Setterfield
2. BERLIN, GERMANY - MAY 13: Jadon Sancho of Borussia Dortmund celebrates with the trophy after winning the DFB Cup final match between RB Leipzig and Borussia Dortmund at Olympic Stadium on May 13, 2021 in Berlin, Germany. Sporting stadiums around Germany remain under strict restrictions due to the Coronavirus Pandemic as Government social distancing laws prohibit fans inside venues resulting in games being played behind closed doors. (Photo by Martin Rose/Getty Images)
Manchester United are in pole position for signing Jadon Sancho and the talks between the Red Devils and the Borussia Dortmund star’s agent are already underway. (Sport1) (Photo by Martin Rose/Getty Images) Photo: Martin Rose
3. City ready Mendes bid
Manchester City are preparing to bid £52m for Sporting Lisbon's Nuno Mendes. (Daily Mail) (Photo by Jonathan Moscrop/Getty Images) Photo: Jonathan Moscrop
4. PSG after Salah
PSG have already been in touch with Mo Salah’s camp, presumably trying to find out whether the Liverpool player would be interested in a move to France. (L'Equipe) (Photo by Laurence Griffiths/Getty Images) Photo: Laurence Griffiths
5. Burnley and Brighton to battle for Man United player
Sunderland have made an offer to Manchester United youngster Jacob Carney with Brighton and Burnley also in the running. (The Sun) (Photo by Catherine Ivill/Getty Images) Photo: Catherine Ivill
6. Alderweireld wanted in Belgium
Tottenham defender Toby Alderweireld is a dream signing for Club Brugge this summer but is delaying a decision on his future. (Voetbal 24) (Photo by Clive Brunskill/Getty Images) Photo: Clive Brunskill