Falcao opened the scoring for the visitors to Istanbul shortly before the half-hour while Hulk's brace sealed an emphatic win in the second half.
Bobo pulled one back at the death for the Turkish hosts but by then the writing was on the wall.
Porto's victory was achieved despite playing the entire second period a man light following Maicon's red card on the stroke of the interval for a professional foul on Besiktas forward Bobo.
With two minutes remaining, their night was further soured when Francisco Fernando picked up a second yellow card.
The win preserves Porto's 100% record in the group phase and all but secures them safe passage to the next round after three games, while Besiktas remain in second place on six points.
Besiktas have been without star men Ricardo Quaresma and Guti in recent weeks and their absence has been keenly felt in that time, with the team slipping to consecutive defeats.
They started this match well enough, however, with Nihat Kahveci's header forcing a good save from Porto goalkeeper Helton inside three minutes.
But Bernd Schuster's side soon found themselves a goal down. A set-piece did the damage, Fernando Belluschi's corner-kick met with a firm header by Falcao from six yards.
Rodrigo Tabata went close to pulling the hosts level a minute later but saw his right-footed effort kept out by the alert Helton.
Porto's night took a turn for the worse a minute before the break when Bobo got goalside of Maicon, and when the defender hauled down the attacker there was only going to be one outcome, the referee brandishing the red card.
Despite their disadvantage the Portuguese visitors extended their lead 14 minutes into the second half, Jorge Rolando picking out Hulk with a long-range pass which the Brazilian forward dispatched beyond Hakan Arikan with a strong finish.
Hulk doubled his tally with a thumping finish into the top-left corner of the Besiktas goal 13 minutes from full-time.
Porto found themselves down to nine men in the 88th minute when Fernando handballed and received a second yellow card for his trouble.
Given Besiktas' numerical superiority it came as little surprise when they got on the scoresheet in the dying moments, Bobo guiding home Tabata's cross from close range, but it was scant consolation after a hugely disappointing display by the hosts.