The Portuguese champions had their moments, striking the woodwork three times and missing a first-half penalty, but bowed out of the tournament and into the Europa League, with Zenit St Petersburg finishing runners-up despite losing 4-1 to Austria Vienna on Wednesday.
Diego Simeone's side rolled into the last 16 of Europe's premier club competition unbeaten in their six games and with 16 points - a record only equalled by their neighbours Real Madrid.
Atletico had guaranteed top spot in the pool a month earlier and Simeone used the occasion to field non-regulars such as 19-year-old midfielder Oliver Torres and former Liverpool full-back Emiliano Insua, with Costa, Miranda, Gabi and Koke the only regular first-team players to start.
Porto, meanwhile, had to win and hope Austria Vienna could do them a favour. The Austrians completed their part of the bargain, but it was no use as Atletico proved that, even when under-strength, they should not be under-estimated.
It was little surprise that the visitors started stronger and had the first attempt on goal, Jackson Martinez hitting the crossbar when sliding in to meet a cross.
But it says a lot about the form Atletico are in at the moment that they took the lead despite making an indifferent start. Garcia took one touch to control the ball by the byline and spun round to hit the underside of the crossbar, the ball bouncing across the line and into the net.
Lucho Gonzalez responded with a shot that was comfortable for Dani Aranzubia to save, and then Silvestre Varela hit the outside of the post.
Porto were presented with an ideal chance to equalise when Aranzubia tripped Martinez after a defensive mix-up, but the goalkeeper was only given a yellow card and stayed on the pitch to dive to his left and save the spot-kick from Josue.
Atletico almost made their opponents pay, Costa racing clear into the area but failing to beat goalkeeper Helton Arruda.
The next time Costa was put through, this time by an exquisite ball from Torres, he made no mistake, flicking the ball past Helton and slotting into the empty net from a tight angle.
With Atletico enjoying a comfortable lead they dropped their intensity after the break, their only chances a Koke corner which almost crept under the bar, and an effort from Garcia that Helton got in the way of.
Even as the game went on and the need for goals became more and more urgent, Porto were unable to break down their hosts, although substitute Lica struck the post.
Porto eliminated Atletico from this competition at the last-16 stage in 2009 but will not be joining them in Monday's draw, in which most teams will be hoping they avoid Simeone's men.