Neymar was rested by Unai Emery after his birthday celebrations at the weekend but PSG did not miss the Brazilian as they remained on track to win the tournament for the fourth year in a row.
Di Maria starred in Neymar's absence, opening the scoring in the first minute by nodding in Kylian Mbappe's cross, and the Argentina international added two more in the second half.
Sochaux had drawn level thanks to a fine finish from Florian Martin, but the gulf between the sides was evident and, after Edinson Cavani put the Ligue 1 leaders back in front, PSG could have made the scoreline even more convincing.
Di Maria struck a brace in a demolition of Rennes earlier in the tournament and Ligue 2 side Sochaux struggled to cope with him and Mbappe, PSG winning their 21st successive Coupe de France match at a canter, despite Kevin Trapp's red card meaning Dani Alves had to go in goal.
Emery had withdrawn January signing Lassana Diarra, Cavani and Marco Verratti for the closing stages, with PSG having one eye on next week's Champions League last-16 tie with Real Madrid as they continue their quest for a quartet of major titles.
PSG took just 54 seconds to score the opening goal, Di Maria on target with a back-post header.
Florian Tardieu lost possession in his own half with PSG immediately springing into attack and Mbappe picked out the Argentine for a simple close-range finish.
Tardieu and Florin Berenguer came close to levelling and Sochaux's strong response to falling behind earned a deserved equaliser in the 13th minute as Martin thumped home after Verratti wasted two opportunities to clear.
Di Maria should have restored PSG's lead but somehow failed to get any contact on Mbappe's low ball two yards out, but Cavani would soon get the holders back on track.
PSG's record goalscorer tapped in at the back post from Layvin Kurzawa's left-wing cross after Di Maria had split the Sochaux defence and Thiago Silva headed against the crossbar after 40 minutes as the chances continued to come.
And PSG effectively wrapped up their victory in the 58th minute, Verratti playing a neat one-two with Julian Draxler to carve Sochaux apart, Di Maria finishing well across Lawrence Ati for his second of the night.
Within four minutes Di Maria had claimed a match ball for the first time since 2010, capitalising on Ati pushing Cavani's powerful shot into the danger zone by flicking the loose ball home.
Di Maria could have had a fourth but kneed another Mbappe cross wide after 76 minutes, while substitute Javier Pastore failed to convert an impudent chipped centre from his compatriot to make the scoreline even more emphatic.
Trapp was perhaps harshly dismissed for catching Thomas Robinet after racing out of his box, meaning Alves had to take the gloves for the final few seconds, but PSG's place in the quarter-finals was never in doubt.