Porto hit the woodwork twice in the first 10 minutes, with the powerful Hulk sending a deflected shot against the bar and then firing a ninth-minute penalty against the post after Kleber was brought down by central defender Yaroslav Rakitskyi.
"We were not lucky but reacted well... stayed calm and waited for the right moment," Porto coach Vitor Pereira said.
"Shakhtar were a high quality opponent but we controlled the game completely," he added.
"No one was expecting that shot because it was from quite far away but I saw the keeper left a bit of space open. It's something we practice during the week, a set piece can decide a match," the Brazil forward said.
Shakhtar's Yaroslav Rakitskiy was dismissed in the 40th minute for a fierce tackle on Joao Moutinho and Porto piled on the misery six minutes after the break.
"We played a good match, managed to keep the ball and it was balanced but two of our players were sent off and the game became complicated for us," Shakthar's Luiz Adriano said.
