Italy held off a superior Spain side for most of the match in Enschede, but struggled to create many chances and lost to a late goal by substitute Joselu.
The victory, which took Spain to their second consecutive Nations League final, was a welcome relief for De la Fuente, who had come under pressure after losing his second match in charge, 2-0 to Scotland in a Euro 2024 qualifier in March.
The Germans, who played two draws against Italy and England on June 4 and on June 7 in the Nations League A Group 3, face Hungary in Budapest on Saturday before taking on Italy on June 14.
Wales manager Ryan Giggs had his bail extended on Friday after he was arrested on suspicion of assault.
Italy have been drawn to face Spain while Belgium will meet France in the last four of the Nations League finals.
Loew is not in danger of losing his job after they were thrashed 6-0 by Spain in their final Nations League group match on Tuesday, Bierhoff has said.
Sancho says his form has dipped slightly this season but dismissed suggestions that it is due to media speculation about his club future.
Croatia kept alive their hopes of reaching the Nations League finals after a stoppage-time winner by left back Tin Jedvaj gave them a 3-2 win over Spain in an electrifying Group 4 clash on Thursday.
England wasted several gilt-edged chances as they were held to a 0-0 draw away to World Cup runners-up Croatia in a Nations League top-tier Group 4 clash behind closed doors on Friday.
European soccer's new Nations League competition will give national team football a boost when it gets under way next month, UEFA President Aleksander Ceferin said on Thursday.
The inaugural UEFA Nations League will pay up to 76.25 million euros ($94 million) in solidarity and bonus fees to the 55 teams participating in the competition, European soccer's governing body said on Friday.
CONCACAF's governing council has agreed to launch a new Nations League tournament, for teams in North and Central America and the Caribbean.