The Australian striker achieved the feat against English club Portsmouth in a pre-season clash in Washington which the home side ended up winning 4-0.
Allsopp's first goal came in the 21st minute from a header from the six yard box before he finished with ease from close range soon after for a second.
His third came in the 65th minute after Pablo Hernandez had put DC 3-0 ahead in a match that saw some very strong challenges and some controversial refereeing.
"An appalling performance from the referee -- appalling," said Portsmouth coach Steve Cotterill.
"I can't believe he's been allowed to officiate a game. I've never seen two players sent off for arguing -- arguing. They were probably six feet away from each other. I've never seen anything like it in my life. Appalling."
United's Curt Onalfo added: "I knew what [Portsmouth's] tactics would be -- they're in preseason, they're tired.
"Once we found our rhythm and started going at them, they decided to foul us on every other play, and that's the job of the referee to realize that. It's not that difficult to see."