Carlos Vela crept in at the near post to tap Real Sociedad ahead on the stroke of halftime but Granada came out fighting in the second half.
After having a goal ruled out for offside, Colombia striker Adrian Ramos headed in the first goal of Adams’ brief tenure in the 65th minute.
Ramos narrowly failed to connect with a cross a few minutes later but Real Sociedad soon made their quality shine through.
Juanmi smacked the bar from the edge of the area and Mikel Oyarzabal wasted a glorious chance before Juanmi volleyed in a clever chipped pass from Sergio Canales to inflict a fifth straight defeat on Granada.
Granada, who were promoted to La Liga in 2011 for the first time in 25 years, are 19th in the standings on 20 points, joining basement club Osasuna in the Segunda Division next season.
Tony Adams speaks after disastrous first game in charge of Granada
Sporting Gijon, 18th with 24 points, have a mathematical chance of survival although they are six points behind 17th-placed Leganes, who have a game in hand.
Later on Saturday Real Madrid host Valencia, while leaders Barcelona make the short trip to local rivals Espanyol.