The fixture had been pushed back from the first round because of World Cup call-ups, finally giving both sides their first points of the campaign on the line.
Riquelme broke the deadlock in the 63rd minute, sweeping home first-time after Cucho Hernández picked him out following a driving run from Antony. Isco, introduced five minutes earlier, almost doubled the lead soon after but saw his effort cleared off the line.
Manuel Pellegrini was pleased with how his side controlled the game from start to finish, telling Movistar LaLiga: "It was a very intense match from the start. We had to bring intensity, because we were at home, and win the ball back. We were very good over the 90 minutes.
"In the first half we lacked precision in the final third. I was very happy with the game overall, especially as it was the first of the season."
The Betis coach acknowledged Real Sociedad's response after going behind.
"We scored the goal and after that they had two chances," he said. "But we also had one from Isco, one-on-one with the goalkeeper, where we could have finished the game at 2-0."
Asked about Isco's role and the club's other new arrivals, Pellegrini explained his management of the returning midfielder's game time.
"We know the quality he has. He's good for 30 minutes a game," he said. "Facundo had a good match, maybe he felt the pace in the second half. In terms of how the team functioned, I was very pleased."
Facundo Bernal impressed on his LaLiga debut in midfield, one of the changes to a Betis side that has strengthened its squad this summer.
Pellegrini also gave an update on players who missed the game, including new signing Troy Parrott, and are working their way back for Tuesday's fixture.
"Parrott comes in already having done pre-season, so he'll be able to play on Tuesday," he said. "I don't think Lo Celso will be ready. We'll see how some of the players recover. Tomorrow we'll start thinking about the next opponent."
Pellegrino Matarazzo felt his Real Sociedad side did not deserve to leave Seville empty-handed, pointing to a missed chance for forward Orri Óskarsson to equalise as the game moved into its closing stages.
"I think we competed well and that we didn't deserve to lose the game, especially given the chance that Óskarsson had to equalise," the Real Sociedad coach said. "In the first half we lost too many balls and didn't have as many chances as we wanted, but we controlled the game until the first goal. After that we took more risks and conceded chances, but we also had our own, and I don't think we deserved to lose."
Despite the defeat, Matarazzo took a broadly positive view of his side's first outing of the season.
"Yes, we lacked the goal, but we're at the start of the season and there's a lot we can take from this game, like the fact that we defended in a compact way, even if we can play better and score goals."
Asked whether he was expecting further signings before the transfer window closes, the Real Sociedad coach played down any immediate incomings.
"No, we're focused on the next match, because with today's team we can compete against anyone, including Real Madrid," he said. "We'll see if we can put in a big performance and get a good result."
The result gives Pellegrini's side, who return to the Champions League this season for the first time in 21 years, a winning start to his seventh campaign in charge, while Real Sociedad will look to bounce back when they return to action in midweek.