Sergio Ramos scored a second-half penalty to help Spain beat a spirited Norway 2-1 on Saturday in their opening Euro 2020 qualifier, while teenage striker Moise Kean netted in Italy's win over Finland.
Spain were not at their clinical best in Valencia, but got their Group F campaign off to a solid start despite Norway threatening an upset.
The 2010 World Cup winners have been unpredictable of late, having been dumped out by Russia in the last 16 of the World Cup and then missing out on the Nations League finals after a home loss to England.
"The team responded well to their equaliser. You always have the dream and aim of achieving something important," Ramos told Spanish television channel TVE. "We're in a new stage with a coach who has a fantastic style of play. We'll take things game by game. We'll pick up more confidence from winning."
Coach Luis Enrique named an attacking line-up, with Marco Asensio, Alvaro Morata and Rodrigo all starting, and it was the latter who volleyed home the opener from Jordi Alba's cross in the 16th minute.
Norway started to grow into the game and were handed a chance to draw level in the 65th minute when Inigo Martinez grabbed Bjorn Johnsen, and Bournemouth striker Joshua King stepped up to slot past David de Gea.
Spain wasted little time in getting their noses back in front, though, as Jarstein felled Morata to concede a 71st-minute penalty. Centre-back Ramos stepped up and confidently dispatched a 'Panenka' spot-kick down the middle to score his 16th goal of the season for club and country.
In Udine, Juventus youngster Kean, 19, became the youngest striker to start for Italy in more than a century as Roberto Mancini's men saw off Finland 2-0.
Italy got off to a flying start as Nicolo Barella gave them a seventh-minute lead with his maiden international goal. The 22-year-old Cagliari midfielder hammered home a low volley after a free-kick was only half-cleared by the Finnish defence.
The day belonged to Kean, though, as he slotted in the second with 16 minutes to play to mark his full debut in style.
"I learn from Cristiano Ronaldo, in training, I steal his secrets," said Keane, who was born in Vercelli, a town between Milan and Turin, to Ivorian parents. "I always try to be ready and train regularly so that I'm prepared when the time comes.
"This is a beautiful evening, but I know that I still have so many records to beat and I intend to beat them.
"To become part of Azzurri history is an added incentive to keep working," said Kean. "There are many goals ahead of me and my aim is to achieve them. I wanted to show that I deserved this chance from Mancini."