Another Brazilian forward, Hulk, put Porto ahead after 13 minutes with a curving free-kick from distance that bounced off the ground before flying past APOEL keeper Dionisios Chiotis, who should have done better.
The visitors levelled with their first shot six minutes later when Ailton received the ball close to the Porto area, dribbled past Fernando and sent a fine diagonal shot that gave keeper Helton no chance.
Porto were slow, predictable in attack and lacked the fluidity that led them to win the Europa league last season, rarely threatening in the second half.
"We lacked tranquility, wanting to do things too quickly, without patience and with little confidence in exchanging passes," coach Vitor Pereira said.
After the equaliser the Portuguese side dominated but APOEL always looked dangerous and midfielder Constantinos Charalambides sent a free-kick from the right that defender Marcelo Oliveira headed just wide on the half hour.
After 63 minutes, in one of the few chances of the second half, Argentina defender Nicolas Otamendi lost the ball in dangerous territory to APOEL's Nuno Morais who ran with it and fired a strong shot that Helton struggled to save.
"We could have done things better and lacked intensity. We knew they were going to be a tricky team," said Porto midfielder Joao Moutinho.
Kleber almost snatched the three points in injury-time, reaching substitute Silvestre Varela's cross just late but moments later APOEL substitute Aldo Adorno was denied the winner at the other end by a fine block from Helton.
The draw keeps APOEL top of Group G on five points, one ahead of Zenit St Petersburg, who drew 2-2 at Shakhtar Donetsk. Porto are also on four, with Shakhtar on two.
"The group is wide open and we have to rectify this result by winning in Cyprus in the next match," added Pereira.
