Police say Dunn had a blood-alcohol level more than twice the legal limit for drivers and was going as fast as 140 mph before the one-car crash.
Hartwell, 30, of West Chester, was a recently married, Iraq War veteran.
His parents, George and Arma Hartwell, of Melbourne, Fla., are suing Dunn's estate, based in Media, and the tavern owner, Barnaby's West Chester, Inc.
The wrongful death suit, first reported in Courthouse News, was filed in Philadelphia Court of Common Pleas. It seeks unspecified punitive and compensatory damages.
The suit alleges that Barnaby's was obligated under Pennsylvania law to refuse to serve clearly drunk patrons, such as Dunn.
Dunn was "visibly intoxicated" at the bar, the suit alleges.
Dunn had a love of fast cars, and a history of citations for reckless driving. He was arrested for driving under the influence in 2005 in Chester County, but the charge was dropped.
Hours before the crash, Dunn posted a photo to his Twitter account showing himself drinking with two other men. Unidentified friends told the celebrity gossip website TMZ.com that Dunn had consumed at least three beers and three shots of liquor at Barnaby's late that Sunday.
At the time, Barnaby's bar manager Jim O'Brien said Dunn came in late the night of the crash with friends, but did not appear drunk.
The suit also names the administrators of Dunn's estate, Andrew J. Donaghy and Ronald Dunn.
The Soloff and Zervanos law firm is representing Hartwell's parents in the suit, which states that the family suffered not only the loss of their son in the crash, but costs such as funeral expenses and medical services.
The suit also says that the estate lost Hartwell's future earnings and wages.