Pedro has been in fine form for his country in recent months and his 58th-minute effort in a tight game at the Stade de France was his 10th goal in his last six starts.
He collected the ball on the right, cut inside and lifted a pass out to Nacho Monreal on the left before surging into the penalty area to bundle Monreal's low centre past France goalkeeper Hugo Lloris.
"Pedro is very important for us because he compliments the passing of Xabi Alonso, Xavi and [Sergio] Busquets with his explosive, dynamic movement," Del Bosque told a news conference.
"We still have three matches to go when both France and ourselves could slip up but we are definitely in an advantageous position," he added.
"The three points were the important thing and also that the players passed this test of their maturity."
Spain were under pressure after Friday's 1-1 draw at home to Finland left them two points behind France, who held Spain to a 1-1 stalemate in Madrid in October, with four games left.
Xavi for the visitors and Franck Ribery for the home side had excellent chances in the first half before Pedro edged Spain ahead and they were able to shut the game down with some controlled possession.
"It was crucial to win here," Pedro said in an interview with Spanish television.
"We could not slip up and I am pleased with the way everything turned out," added the 25-year-old, who now has 12 goals in 26 appearances for Spain.
"I arrived on the run, touched the ball and it went in but I am not really sure how I did it."
Spain now begin their preparations for the Confederations Cup in Brazil in June. Their next World Cup qualifier is away to Finland in September and they play their final two games at home to Belarus and Georgia in October.
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