Neither captain Iker Casillas in the Spain goal nor his England counterpart Joe Hart were much troubled before Cesc Fabregas lifted the ball over the England defence for Gaspar to strike in the 72nd minute at the Jose Rico Perez stadium.
The Villarreal defender, who scored on his debut in a 1-0 Euro 2016 qualifying victory against Ukraine last month, watched the ball come over his shoulder and swivelled to hook it brilliantly past Hart into the far corner.
Juan Mata had a chance to double Spain's lead four minutes later when he was through on goal but Hart did well to block his effort before Nolito teed up Cazorla to stroke the ball into the bottom corner six minutes from time.
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Spain's quality shone through against a drab England, whose unbeaten streak of 15 matches came to an end with their first defeat since a 2-1 reverse to Uruguay at the World Cup finals in Brazil last year.
"I tried to finish off the attack and the ball just went where it had to go," Gaspar told Spanish television. "It was one of the best goals of my life."
England are one of only six nations with a winning record against Spain but predictably found themselves chasing the ball for long periods.
Diego Costa had Spain's best chance before the break when he was picked out by Chelsea team mate Fabregas but curled his effort narrowly wide.
England managed to carve out several openings but their finishing was poor and Gaspar's goal gave a dominant Spain a deserved lead.
England coach Roy Hodgson brought captain Wayne Rooney on for the final quarter of an hour, the Manchester United forward winning his 108th cap to draw level with Bobby Moore in fourth on the appearances list.
Rooney almost grabbed a consolation in the dying moments but his effort hit the crossbar.
"It's a prestigious result against a powerful and strong team," Spain coach Vicente del Bosque told a news conference.
Spain's seventh straight victory was somewhat soured after Thiago Alcantara was forced off midway through the first half with a knee problem and the Bayern Munich midfielder will have tests on Saturday.
(Writing by Iain Rogers, editing by Ken Ferris/Greg Stutchbury)
