Leeds created a host of chances in an extremely dominant first-half display but only had a smart finish from Rodrigo to show for their efforts.
However, the floodgates well and truly opened in the second-half in which Rodrigo struck twice more to complete a hat-trick.
Whites no 9 Patrick Bamford also helped himself to a brace before Robin Koch ensured the Italians were hit for six when heading home in the 90th minute.
The victory for Leeds was not without alarm as Cagliari recovered from 3-0 down to trail just 3-2 by netting twice inside three minutes through Gianluca Lapadula and the impressive Zito Luvumbo.
Graham Smyth, the YEP’s chief football writer, hands out the scores from the friendly that fell six days before the Premier League opener at home to Wolves.
7. Marc Roca
6 - Pressed well, high up the pitch and was tidy on the ball in the main. Tried to get forward. Another who couldn't stop visitors from causing issues on the break. Photo: Chris Hyde
8. Brenden Aaronson
8 - Loads of running, some good link-up play, got involved in attacks to good effect. Put Rodrigo's hat-trick goal on a plate, assisted Bamford and Koch too. Photo: Bradley Kanaris
9. Jack Harrison
8 - A thorn in Cagliari's side with his running and dribbling. When the game became stretched he was a serious threat. Sent in some wicked corners too. Photo: James Worsfold
10. Rodrigo
8 - Got off to a slow start in terms of final third decision making but came to life and fully deserved his hat-trick. Showed his intelligence, made a few chances too. Photo: Chris Hyde
11. Patrick Bamford
8 - Worked hard enough to deserve his goals. Played a part in other goals too with clever contributions in and around the area. Looked sharp. Photo: Bruce Rollinson
12. David Coote (referee)
8 - Refereed it smartly, using his cards when he needed to. Very little controversy in the game. Photo: Nigel Roddis