The 23-year-old had a pivotal role in proceedings on Monday, setting up Valencia's first before finding the net himself with a penalty.
His display was soured somewhat in the 73rd minute, however, as he was shown a second yellow card for a foul on Sergio Escudero.
The visitors came into the game on the back of two successive league wins and made it three on the bounce in style to move two points behind leaders Barcelona, with 10 points to their name after four matches.
Rodrigo assisted the opening goal in the seventh minute, playing in Paco Alcacer who stretched to finish low beyond Vicente Guaita in the Getafe goal.
Alcacer turned provider 13 minutes later, exchanging passes with Andre Gomes to calmly slot into the net from 10 yards.
Valencia were awarded a controversial penalty in the second period when it appeared that Sofiane Feghouli had tripped over his own feet, and Rodrigo rubbed salt into Getafe wounds by sending his spot-kick straight down the middle.
A minute later the forward's match was over, though, as he was given his marching orders for a trip on Escudero, but his dismissal came far too late for it to have any bearing on the result.