The surprise leaders ahead of much wealthier rivals Real Madrid and Barcelona, Atletico are well placed with five games left to become the first club other than the big two to win Spain’s domestic league since Valencia in 2004.
Barca surrendered second place to Real on Saturday when they followed up Wednesday’s Champions League elimination at the hands of Atletico with a shock 1-0 defeat at Granada and Real thumped Almeria 4-0 at the Bernabeu.
Atletico have 82 points, with Real in second on 79 and Barca, who host Atletico on the final day of the season, on 78.
Atletico showed no sign of fatigue at Getafe’s Coliseum stadium following their exertions against Barca, when they reached the last four of Europe’s elite club competition for the first time since 1974.
They last won La Liga in 1996 with a team featuring current coach Diego Simeone in midfield and remain on course for what would be a remarkable double of La Liga and Champions League.
Centre back Godin, who earlier went close with another header, nodded into an empty net five minutes before halftime after Getafe goalkeeper Jordi Codina came out to meet a Juanfran cross but failed to connect.
Angel Lafita was sent off for hauling Miranda down in the penalty area but Atletico’s top scorer Diego Costa, back in the side after injury, had his 66th-minute spot kick saved by Codina.
Costa slid in to divert an Adriano cross into the net six minutes from time but had to be carried off the pitch on a stretcher after crashing into a post and opening what looked like a deep gash in his left leg.
Sevilla closed to within three points of fourth-placed Athletic Bilbao, who host Malaga on Monday, when a Kevin Gameiro double sealed a 2-0 win at 10-man city rivals Real Betis.
Sevilla have 56 points, with Bilbao on 59 and in pole position to secure a berth in Champions League qualifying for next season.
Betis, who had midfielder Juan Carlos sent off in the 27th minute, are eight points adrift at the bottom of the table and appear doomed to relegation.
Eighth-placed Valencia, who were paired with Sevilla in Friday’s draw for the Europa League semi-finals, won 2-1 at home to strugglers Elche to keep alive their hopes of a place in continental competition.
(Reporting by Iain Rogers, editing by Ed Osmond)