The result ended a poor start to the season for Chelsea, who have raised as many talking points off the field as on it following controversy surrounding the treatment of their medical staff and Terry's half-time substitution in the 3-0 loss
Earlier, Anthony Martial gave United the lead after latching onto Andreas Pereira's pass but Lucas Moura's deflected effort in the second-half made it 1-1.
Virgil van Dijk had a half-volley saved off the line by Marc-Andre ter Stegen five minutes after the restart. Second-half substitute Georginio Wijnaldum got Liverpool's second to continue hopes of a miracle comeback.
The match was played at a frenetic pace from start to finish and Liverpool had a goal ruled out in the first half due to a rather controversial offside call, although none of their players protested it.
Argentina continued to struggle to make any sort of impact in the first half until Di Maria beat Hugo Lloris from more than 30 yards just before the break.
Two goals in the first ten minutes of the match from Hazard and Oscar gave the Blues a comfortable lead but Claudio Pizarro drew one back from the penalty spot. On the stroke ofhalf-time, Costa scored Chelsea's third.
It was a tight and tense first half with Jordan Pickford making decent saves to deny Enzo Fernandez's rasping shot and Cole Palmer's dipping drive from range.
He added a second from the penalty spot early in the second half. David Moyes' men made it more awkward for Aston Villa after Jarrod Bowen's deflected strike found the corner of the net.
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With Chelsea having won both their opening Premier League games against West Ham and Watford and Rovers having won just one of their League One games so far this term, it was hardly a surprise that the Blues dominated the early stages of the
Mario Lemina headed in Pedro Neto's corner for the first of them before Hwang himself leveled it up again after heavy home pressure in the second half.
It was a chance for the likes of Pereira and Anthony Martial to prove themselves and Martial did just that when he beat three Real Madrid players to set Jesse Lingard up at the back post at the end of the first half to give United the lead.