Portugal made 11 changes on the back of its dramatic 2-1 win over Republic of Ireland on Thursday (AEST) and initially looked disjointed in the opening quarter of the contest.
But quick-fire headers from Andre Silva and Otavio put Portugal in control before half-time, at which point Qatar was a player light after Meshaal Barsham's dismissal.
Without talismanic skipper Cristiano Ronaldo, Fernando Santos' side was given a scare when Abdelkarim Hassan pulled one back, though Boualem Khoukhi was next to be sent off and Bruno Fernandes made certain of the win with a late penalty.
Qatar lost 4-0 to Serbia on Thursday (AEST) but made a bright start to its latest friendly and nearly took the lead when Almoez Ali sent an angled shot crashing against the post.
Abdulaziz Hatim then called Anthony Lopes into action, but Santos's men took the lead through their first attempt as Silva headed in Joao Mario's cross from six yards.
Otavio's maiden goal came just 84 seconds later, the Porto attacker climbing highest to guide Goncalo Guedes' centre away from Barsham.
Qatar's hopes of finding a route back into the game were dented when, after a lengthy video assistant referee (VAR) review, Barsham was issued a red card for catching Guedes outside the box.
However, shortly after Joao Mario skied a glorious chance over the bar from close range, the 2022 FIFA World Cup host had one back through unmarked Hassan's header.
Felix Sanchez's side could not build on that goal, though, and Fernandes converted from 12 yards after fellow substitute Diogo Jota was fouled by Tarek Salman inside the box, a decision that led to Khoukhi being dismissed for his protests.