Estrada's strike came in the 64th minute when he linked up with Asier Illarramendi to curl his shot into the top left-hand corner of the goal from 25 yards.
It was Sociedad's second win of the season and moves them into fifth place in La Liga, with Granada still in 15th.
Before kick-off, Granada were boosted by the absence of Sociedad's star midfielder Xabi Prieto, who suffered an ankle injury in Saturday's 1-0 defeat by Sevilla.
The newly-promoted side were looking to record their second league win after beating Villarreal 1-0 at the weekend, which was also the team's first win in the top-flight in decades after back-to-back promotions.
But Granada manager Fabri Gonzalez's hopes of sealing all three points was dashed when Estrada beat goalkeeper Fernandez Roberto with his excellent long-range shot.
Both sides took time to settle down, with the first real chance of the game coming from Sociedad's McDonald Mariga in the 12th minute, but his speculative 25-yard strike flew over the bar.
Sociedad midfielder Imanol Agirretxe was then booked for handling the ball in a scrappy period of play.
The best chance of the first period came when Illarramendi delivered a testing corner, which Inigo Martinez headed from inside the six-yard box, causing Roberto to tip the ball over the bar.
Granada midfielder Daniel Benitez then saw his 20-yard volley caught by goalkeeper Claudio Bravo on the stroke of half-time to leave the scores locked at 0-0.
After the break, the home side had more of the attack, with Carlos Vela's shot missing the target just minutes before Estrada broke the deadlock.
Sociedad continued to press but failed to increase their slender lead, with Granada never looking likely to score.