Barcelona's 4-1 win over Malaga earlier in the night meant Madrid had to win at San Mames in the evening's late game to seal a record 32nd La Liga crown, and they did so comfortably despite missing an early penalty from Cristiano Ronaldo.
Ronaldo, who also missed from 12 yards in last week's penalty shoot-out defeat to Bayern Munich in the Champions League semi-final, saw his attempted dink saved by Gorka Iraizoz in the 12th minute, but within eight minutes of that miss Madrid were 2-0 up and well on their way to ending Barca's three-year reign as champions.
Gonzalo Higuain opened the scoring in the 16th minute with a superb 18-yard effort into the top corner, before Ozil doubled Madrid's advantage four minutes later with a far-post finish from Ronaldo's brilliant low cross.
Ronaldo got on the scoresheet himself five minutes after half-time when he headed home Ozil's corner for his 44th league goal of the campaign to all but end any hope of Europa League finalists Athletic getting back into the match.
Athletic had Spain international Javi Martinez sent off in 72nd minute as Madrid comfortably controlled the closing stages en route to the title-winning victory.
The success means Madrid coach Jose Mourinho, who is in second season at the Bernabeu, has now won league titles in four different countries having been victorious with Porto (Portugal), Chelsea (England) and Inter Milan (Italy).
Earlier, Barca ensured Madrid would have to do it themselves if they wanted to clinch the title this evening as Pep Guardiola's men claimed a convincing victory over Malaga in which Lionel Messi enjoyed another record-breaking match.
The Argentina international netted a hat-trick to set the record for most goals scored in a European season.
Messi scored twice from the penalty spot before wrapping up his treble with a low drive to take his tally to 68 goals for the campaign, passing the previous mark of 67 set by Gerd Muller in 1972/73.
Messi's treble, which sees him leading Ronaldo by two goals in the race to be top scorer in La Liga, came after Carles Puyol fired the home side in front, only for that lead to be cancelled out by Jose Salomon Rondon.
It was also an emotional night at the Nou Camp as Barca played their first home game since Guardiola confirmed his intention to step down at the end of the season.
Malaga's defeat means Valencia were able to take a step closer to securing third spot as they thrashed Osasuna 4-0 thanks to four goals in the last 13 minutes.
Osasuna had been playing with only 10 men since first-half injury-time following the dismissal of Dejan Lekic, and they were unable to hold out as Valencia took the win through late braces from Aritz Aduriz (77 & 87) and Jonas Oliveira (82 & 88).
Valencia are now three points clear of Malaga heading into the final two games of the season.
The good news for Malaga is that they are still three points ahead of Levante, who were beaten 1-0 at relegation-battling Real Zaragoza, for whom Edu Oriol scored the only goal in the 11th minute.
Third-bottom Zaragoza are now only three points behind Rayo Vallecano and safety.
Rayo slumped to their fifth successive loss and eighth in nine games after losing 1-0 at Real Mallorca, Gonzalo Castro's 62nd-minute goal deciding the match.
In the Seville derby, Benat Etxebarria fired home an injury-time free-kick to hand Real Betis a dramatic 2-1 victory and deal a potentially fatal blow to Sevilla's hopes of claiming a Europa League qualifying place.
Hosts Sevilla went into the game without a win in three but made a dream start when Alvaro Negredo struck after six minutes, but Betis drew level through Benat in the 43rd minute before the midfielder netted a last-gasp winner after the home side had Gary Medel sent off.
The result dragged Betis level on points with their neighbours on 46 points but leaves the pair four points off sixth-placed Atletico Madrid, who conceded a last-gasp equaliser to draw 1-1 at home with Real Sociedad.
Gabi put Atletico ahead but the midfielder undid some of his good work by picking up two yellow cards in quick succession to leave his side a man down for the final 17 minutes, and that pressure told as Sociedad striker Carlos Vela scrambled home a 90th-minute equaliser from only a yard out.
Congratulations To The Players, Fans & Most Especially Jose For Bringing Back Spanish Glory Back To The Capital.. Have Your Say Pals..
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