Alvaro Morata opened the scoring for Spain with a 33rd minute volley but Greece found an equaliser via a curious penalty where Inigo Martinez’s sliding clearance turned into a late tackle on Giorgos Masouras.
Anastasios Bakasetas stepped up and converted past Spain keeper Unai Simon for the equaliser, with Spain’s best chance after coming from a Morata header.
“We did not expect this result, we did not deserve it. A fair result would have been the one that was on the scoreboard before Greece’s goal,” Luis Enrique said.
“We deserved another result, although we did not create the flow of opportunities or have the finesse to score goals against a team as organised as Greece.”
Sweden beat Georgia 1-0 in the other Group B game with Viktor Claesson netting the winner.
First-half goals to Domenico Berardi and Ciro Immobile helped Italy to a 2-0 victory over Northern Ireland in Parma in Group C.
Switzerland triumphed 3-1 away to Bulgaria in the other Group C match, scoring three goals inside the opening quarter of an hour.
In Group I, England eased past minnows San Marino 5-0 with debutant Ollie Watkins among the scorers.
Everton’s Dominic Calvert-Lewin netted a double while James Ward-Prowse and Raheem Sterling also scored.
Albania beat Andorra 1-0 and Hungary and Poland drew 3-3 in the other group games.
In other significant results, Denmark won 2-0 in Israel, Scotland drew 2-2 with Austria and Germany cruised past Iceland 3-0.