They now need only a point in their final two games of the Premier League season to ensure they finish in the top four.
Liverpool, who had been chasing their arch rivals after relentless winning run of late, drew with Aston Villa at Anfield to lose ground in the race.
De Gea made a series of excellent saves on the south coast to preserve United’s lead after Casemiro’s early overhead kick.
The Spaniard has come under increasing criticism in recent weeks and months after a number of errors but ten Hag believes he underlined his importance at the Vitality Stadium.
"David de Gea made a mistake a few weeks ago but everyone can make mistakes,” said the Dutchman.
“We defend with 11, that’s why we have so many clean sheets. David made some great saves.”