- Brais Méndez (4')
- Lautaro Martínez (87')
The Basque team looked the more dominant side for most of the game,their first Champions group-stage appearance in a decade, while the Serie A leaders will be grateful for their rivals' misses in front of goal after a performance far from their unbeaten league run.
"I have congratulated my boys for the great game they played," La Real coach Imanol Alguacil told Movistar Plus. "The players, the fans and myself should be proud."
The hosts' early high pressing paid off after just four minutes when Brais Méndez stole the ball on the edge of the Inter box to fire into the bottom right corner and make it 1-0.
Real created chances to double the lead, but Robin Le Normand sent his header wide before half-time and new keeper Yann Sommer pulled off a great save to deny Mikel Oyarzabal from close range at the start of the second half.
"We faced a very strong side tonight, we knew it," Inter coach Simone Inzaghi told Amazon Prime. "We did well to remain in the game despite playing badly, thanks to our goalkeeper."
Inter began to threaten their opponents' area until the final stretch of the match, but could not equalise until Martinez finally scored in the 87th minute for his sixth goal in five games this season.
"I'm not satisfied because we did not play as we planned," Martinez said. "We had a lot of troubles in the first half because we were facing a team who pressed us very high and we had difficulties to build from the back with the forwards often going offside.
"We did not play well but it was important to avoid defeat at least because the group would have become more complicated otherwise."
- Michael Oliver