A mixture of poor finishing from La Roja's players and good goalkeeping from Rune Jarstein had the home side frustrated in Valencia.
Joshua King put Norway on course for a shock point when converting from the penalty spot to cancel out Rodrigo's opener, but Ramos earned his side a deserved victory that gets them back on track following a disappointing 2018.
Norway keeper Jarstein was a busy man in the first half as he was regularly called into action to keep out the opposition, who had 15 attempts in total before the interval, seven of those on target.
Alvaro Morata had three good headed opportunities kept out, sending two of those right at Jarstein and forcing the overworked stopper into a good save from the third of them.
Either side of those misses, Rodrigo edged the hosts in front with a pretty simple finish from the edge of the six-yard box, profiting from some good play by Jordi Alba down the left-hand side.
Rodrigo was denied a second by a smart stop from Jarstein, nearly picking out the bottom corner with his flicked finish, and Daniel Parejo also came close from a long-range free kick that was on target.
For all Spain's dominance, though, with Ramos almost diverting a miscued Sergio Busquets volley into the back of the net and Alba having a goal ruled out for offside, Norway squandered a glorious opportunity of their own.
Marco Asensio and Morata were also unable to find a way past Norway's inspired keeper, with the former's powerful drive being pushed aside and the latter being similarly frustrated down low.
Incredibly, after Ramos became the latest to see a chance come and go, Norway managed to level up the match through a King penalty.
King made no mistake from 12 yards, but Spain were back in front six minutes later as Ramos converted a penalty of his own - a cheeky Paneka down the middle - after Jarstein raced off his line and wiped out Morata.
Norway committed bodies forward late on to set up a nervy finish to the match, but the final two chances of the match fell the way of Asensio, who clipped the ball over the bar from one and was kept out by Jarstein from the other in a fitting conclusion to the game.
SPAIN (4-3-3): De Gea; Navas, Ramos, Martinez, Alba; Parejo, Busquets, Ceballos; Rodrigo, Asensio, Morata
NORWAY (4-4-2): Jarstein; Elabdellaoui, Nordtveit, Ajer, Aleesami; Odegaard, Henriksen, Selnaes, Johansen; King, T.Elyounoussi