Getafe looked like the better side out of the gate and didn’t have to wait too long to break the deadlock, as Rodriguez took advantage of the first chance he had to find the back of the net inside eight minutes.
The Real Madrid loanee nodded home a perfect cross from Luis Milla to notch his second goal of the campaign while giving the hosts an early lead.
Espanyol attempted to push up the pitch in an attempt to regain a foothold in the contest, but their lack of ideas prevented them from posing a threat near David Soria’s goal.
The hosts often found spaces in their opponent’s porous defensive line, but despite edging their rivals 5-0 in shots on target, they only had one goal to show for their supremacy after the opening 45 minutes.
In an attempt to turn things around, Espanyol boss Manolo Gonzalez sent Walid Cheddira onto the pitch for the second half, with the tactical change leading to two strikers playing up top for Los Pericos.
The substitute was inches away from equalising following a low cross, but he couldn’t tap the ball home from inside the six-yard box.
Alex Kral also came close to drawing the visitors level but his effort flew wide following a deflection in a Getafe defender.
The second half was far more intense than the first, as both teams found more spaces going forward, and while it translated to an uptick in scoring opportunities, neither side managed to find the back of the net.
Ultimately, and despite their second-half improvements, Espanyol fell to another loss, their 10th of the league campaign, leaving the Catalan outfit in the relegation zone.
Victory creates a gap from the bottom three for Getafe, with the Madrid-based side three points above their opponents who remain in 18th place.