Fernandez’s thumping header early in the second half settled a bruising London derby at Stamford Bridge.
Manchester City and Newcastle had both won on Wednesday to knock Chelsea from fourth down to sixth in the race to qualify for next season’s Champions League.
But Chelsea’s response lifted them one point clear of fifth-placed City and two ahead of sixth-placed Newcastle.
The top four are guaranteed to reach the Champions League, with fifth also likely to secure a place depending on the results of the English clubs left in European competitions this season.
Chelsea, who have now lost just one of their past 13 league games against Tottenham, had been far from convincing recently, with boss Enzo Maresca criticised for his cautious tactics.
Beaten 1-0 at Arsenal in their last game before the international break, Chelsea’s players had a planned day off cancelled by Maresca due to a poor effort shown during an informal match against one of the club’s youth sides.
The Blues were more dynamic against Tottenham, but still lacked a cutting edge despite holding on for a fifth win in their last six games in all competitions.
For Postecoglou, it was another dispiriting loss in a wretched season that could end with his sacking.
Tottenham are without a victory in their last four league matches and have won only one of their last six games in all competitions.
The north Londoners are languishing in 14th place after a 16th defeat from 30 league games.
The last time they finished as low as 14th was in 2003-04, while their worst final position in the Premier League era was 15th in 1993-94.
Tottenham fans have grown increasingly frustrated with their side’s decline, staging a series of protests against chairman Daniel Levy.
They turned on Postecoglou as well during the second half, chanting “you don’t know what you’re doing” at the Australian.
Tottenham’s last chance of ending their 17-year trophy drought and fulfilling Postecoglou’s boast that he always wins a major prize in his second season lies in the Europa League, where they face Eintracht Frankfurt in the quarter-finals.
Chelsea almost made the perfect start inside the first minute when Trevoh Chalobah’s pass reached Nicolas Jackson, whose shot was saved by Guglielmo Vicario and hit Van de Ven before bouncing off the post.
The Blues were on top in the opening minutes, and Malo Gusto’s blast flashed just wide from the edge of the area.
Vicario had to smother the ball on the goal-line after Fernandez tried to bundle home from Cole Palmer’s deflected cross.
Maresca had urged Jadon Sancho to provide more cutting edge amid mounting criticism of the winger’s spluttering form during his loan from Manchester United.
Sancho nearly rose to Maresca’s challenge with a curling effort that Vicario brilliantly tipped over.
Tottenham defender Cristian Romero pushed Levi Colwill to the ground in a clash that sparked a mass confrontation on the stroke of half-time.
The row seemed to fire up Chelsea, and they finally made the breakthrough in the 50th minute.
Palmer’s cross picked out Fernandez, and the Argentine powered his header past Vicario from five yards.
When Postecoglou sent on Brennan Johnson and Pape Sarr for Wilson Odobert and Lucas Bergvall, Tottenham fans taunted the Australian with derisive chants.
For a few moments, it seemed Sarr had silenced Postecoglou’s critics as he drilled home from long range in the 69th minute.
But the goal was disallowed by VAR for Sarr’s foul on Moises Caicedo, leaving Postecoglou shaking his head in frustration.
Son Heung-min was inches away from rescuing Postecoglou in the 89th minute, only for Robert Sanchez to make a superb save from the forward’s close-range shot. (AFP)
