Ruta del Sol stage one: Puente de Génave › Santiago de la Espada, 179km, Volta ao Algarve stage one: Portimão › Lagos, 200.2km.
Rodriguez sprinted to third in the chase group behind, finishing 38 seconds behind Pogacar on the stage of the race with the most climbing metres.
Tao Geoghegan Hart and Pavel Sivakov were in the next group behind Rodriguez, finishing fifth and sixth respectively to make sure there were three Grenadiers in the top 10.
Pidcock battled for position in a tricky finish which saw the riders battered by a headwind which meant timing was key, with Alexander Kristoff (Uno-X) coming out on top.
Stage two will see another change of pace, with more climbing on the menu and a summit finish to Alto de Foia for the team to contend with.