The Catalan outfit had been looking to bounce back from their 2-1 loss at Manchester United in the Europa League on Thursday evening, which saw them exit the competition.
Barcelona brought a seven-game winning run in the league into the contest, but they were beaten by a first-half Toure goal in what was a highly frustrating game for the division leaders.
The result has left Xavi's side top of the La Liga table, seven points ahead of second-placed Real Madrid on the same number of matches (23), while Almeria have moved into 15th, now two points clear of the relegation zone.
Toure did brilliantly to hold off Eric Garcia before beating Barcelona goalkeeper Marc-Andre ter Stegen on the half-volley, with Almeria shocking the leaders in the 24th minute.
Almeria had two opportunities to score a second in the first period, but Leo Baptistao saw his effort saved by Ter Stegen, before Rodrigo Ely just missed the target with a header.
Gavi had a shot deflected just wide of the post in the 59th minute, before Raphinha just failed to make contact with a Ferran Torres cross 20 minutes from time.
Ronald Araujo was next to try his luck, glancing wide of the post in the 80th minute, and the pressure continued in the latter stages, with Barcelona desperately searching for a leveller.
Robert Lewandowski and Araujo had half-chances in stoppage time, but the best opportunity late on came for Almeria, with Adri Embarba bringing a smart save from Ter Stegen.
Barcelona will be bidding to return to winning ways when they travel to Real Madrid in the first leg of their Copa del Rey semi-final on Thursday, while Almeria will continue their league campaign at home to Villarreal next weekend.