Alvaro Morata's late goal helped Spain qualify for the 2022 World Cup and consigned Sweden to the play-offs.
Sweden goalkeeper Robin Olsen tipped Dani Olmo's shot on to the crossbar with Morata on hand to tap the ball in after 86 minutes.
Luis Enrique's side needed just a point to top Group B while Sweden needed to win to finish above their opponents.
The result means Spain have qualified for a 12th consecutive World Cup finals.
Sweden will have another chance to reach Qatar in the European play-offs in March.