Rui Jorge's side went into the clash knowing that a four-goal victory, or winning by a three-goal margin as long as they scored at least four, would see them dislodge Slovakia as best runners-up and put themselves in pole position to reach the semi-finals.
As a result, the Portuguese wasted no time in chipping away at their four-goal target and found an opener within two minutes of kickoff when Edgar Le got the run on his marker from a corner and powered a low header past Damjan Siskovski.
It was two 19 minutes later when Bruma - who scored a superb volley against Spain last time around - bagged another fine goal, cutting inside Egzon Bejtulai from the left-hand side and curling past a helpless Siskovski from a tricky angle.
There was no time for celebrations as Bruma raced back to the halfway line with the ball under his arm. Portugal meant business, but they suffered a setback in their quest for a last-four spot on 41 minutes when Enis Bardi, against the run of play, beat Bruno Varela from 30 yards with a fine strike.
Macedonia displayed the same signs of resilience early in the second half, but Portugal restored their two-goal lead, and moved within one goal of their target, on 55 minutes when Daniel Podence turned well in the box and finished quickly past Siskovski.
One more goal would have given Portugal a great chance of reaching the knockout stages, but their quest for the semis was made even steeper on 80 minutes when Kire Markoski finished off a swift counter-attack by slotting past Varela for a goal which all but ended Portugal's hopes.
However, Bruma threw his side a lifeline by volleying a fourth into the roof of the net on 90 minutes, but a bizarre straight red card for Diogo Jota, for what looked an innocuous incident, put paid to their hopes of scoring again.