The win takes Marcel Koller’s Austrians to 10 points in the pool after four games played, with a five-point lead over Fabio Capello’s side who suffered the first defeat of their campaign at the Ernst-Happel-Stadion on Saturday evening.
The visitors had several chances to open the scoring but their failure to do so came back to haunt them as Okotie hit the target in the 73rd minute.
It was the home side who started strongly, with Martin Harnik’s drilled effort from just outside the edge of the area going wide.
But the visitors were the ones to come closest to opening the scoring in the early going as Dynamo Moscow forward Aleksandr Kokorin struck a post with his thumping long-distance strike.
Harnik then saw another strike tipped round the post by Russia goalkeeper Igor Akinfeev, but Capello’s men ended the half strongly.
First, Denis Cheryshev wasted a gilt-edged chance by missing the target with his point-blank header and although Sergei Ignashevich did better with his effort, Austria custodian Robert Almer was able to make a superb save.
Russia continued to enjoy the better of the chances after half-time as Dmitri Kombarov fired over the bar before Kokorin headed wide.
Their profligacy was to Austria’s advantage as Okotie opened the scoring with 17 minutes remaining.
The 27-year-old Pakistan-born 1860 Munich forward was able to slot home from Harnik’s teasing cross.
Martin Hinteregger’s stunning volley went over as Austria went in search of a second.
That they were unable to add to their tally was of no consequence as Russia offered little in going forward in the closing stages.