The win leaves Porto second in the group with six points, three adrift of leaders Chelsea but five clear of a struggling Atletico Madrid and APOEL.
"Our position in the table is fair and our wins were fair. Logic may lead us to believe that passing to the next stage is very close... but from experience we know that the final two or three Champions League group match days sometimes produce illogical results," Porto coach Jesualdo Ferreira said.
Porto lacked creativity in the absence of playmaker Fernando Belluschi but Hulk and Falcao compensated with several long-distance shots.
Just as Porto were starting to create flowing moves, APOEL stunned them by scoring with their first attack on 22 minutes. Helio Pinto crossed from the left and, trying to prevent Constantinos Charalambides reaching the ball, Alvaro Pereira deflected the ball into his own net.
INTELLIGENT PORTO
"We needed a strong, serene and intelligent Porto to beat this opponent but things got complicated with their goal," Ferreira added.
The Portuguese champions took 11 minutes to react and equalised when irrepressible Colombian striker Falcao stole the ball on the edge of the Cypriot box and passed to Hulk who scored with a well-placed left-footed drive on 33 minutes.
In the first minute of the second half, Elias handled the ball in the box and Hulk converted from the spot to give the hosts a deserved lead.
"I have no complaints about my players but I think we could have played better. We did make some mistakes and at this level mistakes are costly", APOEL coach Ivan Jovanovic told reporters.
With APOEL failing to pile on any pressure, Porto pressed ahead as they searched for a third goal.
Hulk strode forward in the 52nd minute and squared perfectly for Falcao but the striker sent an easy tap-in wide.
Three minutes later, Falcao and Hulk combined again, with the Brazilian forward's thunderous shot blocked by Dionisios Chiotis.
Porto went down to 10 men when Mariano Gonzalez was sent off for lashing out at Marinos Satsias in the 74th minute but could not be denied the three points.
