The MLS outfit, founded in 2009, made a stunning start to their life in the North American tournament, with two goals in either half in Guyana.
Steve Zakuani fired Portland ahead in the 18th minute after being played through on the left side of the pitch by midfielder Kalif Alhassan.
A stunning effort from a set piece from Barbosa Murillo gave Alpha hope on the stroke of half-time, the Brazilian's strike going in off the underside of the crossbar despite Portland goalkeeper Andrew Weber's best efforts.
The tricks did not stop there, though, as Fanendo Adi flicked Alvas Powell's cross into the net to reinstate Portland's two-goal buffer in the 66th minute.
Powell was on hand to make it 4-1, after Rodney Wallace's cross into a dangerous area was not completely cleared by the Alpha defence - and the unmarked Jamaican tapped in the visitors' fourth.
Caleb Porter's side sit top of Group Five on goal difference from Olimpia, who also have three points after downing Alpha.
America and Comunicaciones both have three points and plus-five goal difference after respective thrashings of Bayamon, but the Mexicans' goals for has them slightly on top of the table.
Justin Arboleda's 70th-minute penalty was enough for the hosts to take all three points, and be two points clear top.
