Ballots from all 67 precincts were counted by 4 a.m. local time on Wednesday.
Unofficial results from the Guam Election Commission reported that Moylan received 17,075 votes compared to Won Pat's 15,427 votes.
Exit polls had Won Pat defeating Moylan by 13 percentage points, but he wound up winning by five percentage points.
Guam delegates elected to the U.S. House of Representatives do not have a vote on the floor. Moylan is the second Republican elected to the non-voting seat since Congress created the seat in 1972.
"I have many aspirations on different measures that we want to introduce, such as SSI," Moylan stated while campaigning for the delegate position. "And different measures to help our police force."
Incumbent Delegate Michael San Nicolas (D) will vacate his seat in January. In August, Nicolas lost to Governor Lou Leon Guerrero in the gubernatorial primary race.
Governor Guerrero and fellow Democrat Lieutenant Governor Joshua Tenorio held onto their seats and defeated their Republican opponents by 11 percentage points in Tuesday's midterm elections. Exit polls predicted Guerrero would win by 25 percentage points.
Democrats gained a seat in the territorial legislature, maintaining a majority with nine seats compared to the six seats held by Republicans.