There was little between the two sides in the first-half in terms of chances, but the home side took the lead on the stroke of half-time when Gassama stroked the ball home.
Tenerife were tasked to break down Fuenlabrada in the second-half, but good chances went begging from Dani Gómez and Nikola Šipčić and the visitors were handed just their second league defeat in their last nine matches.
Fuenlabrada move up into the top half of the table, five points outside the top six, while Tenerife remain 13th and sit four points above the relegation zone.
LaLiga returns after three month break due to pandemic
Only one team - Real Zaragoza - in the league had picked up more points than Tenerife in their last six games, but the coronavirus pandemic brought a grinding halt to world football back in March. It had been over three months since the teams were last in action and, as expected, neither side came racing out the blocks.
Fuenlabrada had the first sight of goal in the 10th minute. Antonio Glauder picked up the ball to the left of centre and sent his shot just wide of the post from the edge of the area.
The visitors were almost caught on their heels six minutes later when Iker Undabarrena’s pass was intercepted by Hugo Fraile deep in his own half. Fortunately for Tenerife, the shot was timid and Adrián Ortolá saw it all the way.
Javi Muńoz had a chance shortly after, but the first clear-cut opening in the game was just before the half-hour mark. Tenerife worked the ball well from left to right. Matías Nahuel picked out Muńoz on the edge of the area, but the defender fired over the bar with his first-time effort.
The Blue and White’s were growing into the game as the first-half progressed and went close on 41 minutes. Gómez made the most of the advantage, following a foul on Undabarrena, and his effort took a slight deflection and went into the side netting.
Fuenlabrada dealt a blow right at the end of the half. A throw-in from the left was glanced on into the path of Gassama, who drove into the penalty area, avoided the challenge and stroke the ball home.
Visitors unable to break down Fuenlabrada in second-half
Going into the second-half, Tenerife were tasked to go in search of an equalising goal. Nahuel couldn’t keep his shot down on 59 minutes, but Rubén Baraja’s side continued to control possession and were on top.
Substitute Suso picked up the ball on the right, in the 74th minute, and crossed to the feet of Gómez. The striker turned his marker on the edge of the area, but couldn’t direct his shot towards goal.
Three minutes later, Tenerife had one of their best chances of the game. Midfielder Luis Milla delivered the corner into the box and Šipčić rose above his marker at the front post and headed just over the bar.
Time was running out for Tenerife and it wasn’t to be on their return to the league as Fuenlabrada saw out the closing stages for an important three points.