The Audi driver got his strategy perfect as he gazumped long-time leader Green in the closing stages of the final meeting of the season, having changed to the option tyres for the second half of the race.
Ekstrom started on the hard tyre, which will be the only available tyre in 2015, and was in ninth place prior to his pit stop, but the Swede began to work his way through the field as soon as he switched to the softer tyre
However, he needed a safety car following Dani Juncadella's crash on lap 37 to help him take the lead.
Ekstrom quickly applied pressure to the leader after the restart as he passed Green after three corners and went on to claim victory, his second of the season after winning at Zandvoort last time out.
Mike Rockenfeller, Ekstrom's team-mate, also came through to claim second, with Green having to settle for third, despite leading for the majority of the race.
The Briton was ahead inside the first lap as Miguel Molina ran wide at the second corner and Green slowly began to open up a lead over Pascal Wehrlein (Mercedes).
Wehrlein's challenge was soon over after an unsafe release saw him incur a drive-through penalty.
That gave Ekstrom the opening he needed and together with Rockenfeller they began to pick off drivers in front of them.
Eventually only Green was ahead of the pair, but catching his Audi team-mate looked tough with a 9.7-second deficit, until the safety car came to his aid.
Mercedes' Paul di Resta followed the three Audi's home in fourth, with newly-crowned DTM champion Marco Wittmann (BMW) in fifth.
Timo Schieder (Audi), Martin Tomczyk (BMW), Robert Wickens (Mercedes), Molina (Audi) and Antonio Felix da Costa (BMW) completed the top 10.
Audi's strong performance at Hockenheim saw them pip BMW to win the manufacturers' championship.