Scotland's World Cup dreams ended by draw in Slovenia
Bezjak equalised with a free-header from a Josip Ilicic free-kick and had yards of space to slot home the second after a corner from the same player.
Bezjak did grab a second and put Scotland behind when he controlled the ball from a corner and had time to slot it through a ruck of bodies and into the corner of Craig Gordon's goal.
The wait goes on for Scotland, who haven't appeared at a major tournament since the 1998 World Cup in France.
England wrapped up their campaign with another Harry Kane-inspired victory, in a duel with Lithuania that saw Gareth Southgate experiment with his line-up somewhat.
Scotland have not made the play-offs and have now been eliminated from World Cup contention after struggling in group F.
Sadly, both are sticks which can be wielded when picking apart a Scotland performance that was woefully short of the required standard in Slovenia.
Already qualified Germany finished a dominant march to Russian Federation with a 5-1 win against Azerbaijan.
Germany, Group C winners, closed their qualifying campaign with a 100 per cent record following a 5-1 win against Azerbaijan in Kaiserslautern. The third goal never came and so the Slovaks claimed second spot on goal difference.
Conceding the second goal presented Scotland with a mountain to climb but the visitors were close to equalising after 78 minutes when Darren Fletcher had space inside the box but blasted his shot high over the crossbar.
The draw for the play-offs takes place on October 17, and it will be seeded, meaning Northern Ireland's result against Norway on Sunday evening is still important if they want to potentially avoid the likes of Portugal, Italy and Wales.
Scotland were unable to keep alive their World Cup dream on Sunday, held to a draw in Slovenia.
A victory over Norway was still important if they wanted to stand a chance of being seeded for that draw, yet Brunt's freaky own goal 19 minutes from time, in which he hacked an attempted left-footed clearance into his net, essentially scuppered those hopes as they lost 1-0.
"We got the goal first half without playing well".
Manchester United midfielder Henrikh Mkhitaryan got himself on the scoresheet with a delightful chip but Bayurzhan Turysbek struck a 61st minute equaliser.