Atletico bounced back from a 4-0 hammering at the hands of Borussia Dortmund in the UEFA Champions League with Godin and Filipe Luis on target either side of half-time.
That loss was the heaviest of Diego Simeone's seven-year spell at Atletico, but his side has now taken 14 points from a possible 18 to climb to the top of Spain's premier competition.
Last season's champion Barcelona can reclaim top spot if it avoids defeat at home to Real Madrid in the first Clasico of 2018/2019, but anything could happen with Lionel Messi out of the game with a broken arm.
Antoine Griezmann's improvised volley flew over the crossbar as Atletico made a slow start in response to its UEFA Champions League humiliation.
Ruben Pardo fired off target twice in quick succession but Atleti took the lead shortly before half-time.
Angel Correa did brilliantly to turn away from Kevin Rodrigues and Raul Navas could only deflect the low cross out for captain Godin to finish smartly into the bottom-right corner.
It was another defender who struck the decisive second goal on the hour-mark.
Filipe Luis, a half-time replacement for World Cup-winning defender Lucas Hernandez who went off as a precaution with a muscle problem, sent a smashing finish into the top-right corner, giving former Atletico goalkeeper Miguel Angel Moya no chance.
Diego Costa fired straight at Moya as Atletico sought to extend their lead, but Simeone and his side can watch El Clasico from a lofty position atop LaLiga.
There is Copa del Rey action for both teams this week, with Atletico travelling to minnow Sant Andreu, while Celta Vigo welcomes Real Sociedad to Balaidos.