The Spanish side travelled to Portugal on the back of seven consecutive La Liga victories this season, while their hosts had not lost at Estadio Dragao in Europe's premier club cup competition since November 2009.
Jackson Martinez lost his marker Godin to head Porto into a first-half lead, but the home side could not capitalise on their superiority before the break and Atletico made them pay.
Godin made amends for his earlier error by equalising before Gabi passed a free-kick into the area for Arda Turan's 86th-minute winner, with the Turk capping off a brilliantly simple set-piece that was apparently Simeone’s idea.
Godin told reporters after the game: "The merit goes to our coach who put the move together.
"We are going game by game - not thinking about winning Liga or the UEFA Champions League – but continuing to work hard."
The Uruguay international was delighted to find the back of the net and is adamant that was the turning point in the match.
He added: "The truth is that my goal was a special one as it brought us back into a game that was a little bogged down.
"You have to tip your hat to our second which came from a strategic move that we had prepared, but until the game didn't have an opportunity to pull it off."
Simeone was quick to congratulate his players for triumphing at a stadium in which Porto had not lost in 35 matches.
"We played an extremely difficult game in a stadium in which few win," the Argentine enthused. "I want to give huge congratulations to the response given by the team from the first to second half."
Atletico now top Group G with two wins from two games.