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.
1. Illan Meslier
7 - Hung out to dry for both goals, the second of which was an absolute beauty. Made a smart save with his only real first half involvement. A bystander for the most part. Photo: Bruce Rollinson
2. Rasmus Kristsensen
7 - Not always accurate with his passing but always an option and always attacking. Added real presence and a right flank outlet that was heavily used. Photo: Daniel Carson
3. Robin Koch
6 - Composed first half, good on the ball. Had the second half in control until he gave Luvumbo too much room for the first and couldn't stop Leeds looking shaky defending counters. Good goal. Photo: James Worsfold
4. Diego Llorente
6 - Similar story to his partner. A very solid first half. Let Lapadula run in behind him for Cagliari's first goal and then looked susceptible to balls in behind. Photo: TREVOR COLLENS
5. Pascal Struijk
6 - Not as offensively gifted as Kristensen but he's a centre-half playing in an attacking left-back position. Plenty of effort, some nice stuff. Being so high did bring a big risk of being caught out by pace. Photo: Chris Hyde
6. Tyler Adams
6 - Lots of industry, some tidy football and intense pressing to keep control of the game in the first hour. Quieter period followed. Photo: Chris Hyde