Teenage full-back John Flanagan provided a testing cross from the right which Mike Williamson only partially headed clear, allowing Rodriguez to volley a shot from 12 yards that took a crucial deflection off Danny Simpson past keeper Tim Krul.
The others are Leicester duo Anthony Allen and George Chuter, Wasps pair Joe Worsley and Tim Payne, Gloucester's James Simpson-Daniel and Paul Doran-Jones, Saracens wing David Strettle and Harlequins flanker Chris Robshaw.
Myler's second successful conversion put Northampton 20-14 in front at the break and Gloucester reshuffled their back division for the second half, with Simpson-Daniel moving into midfield instead of Tim Molenaar and Charlie Sharples slotting in on the wing.