After missing their chance to clinch top spot in Group D with a defeat to Austria last week, Serbia made amends at the second attempt with a crucial victory to clinch their World Cup ticket.
Aleksandar Prijovic scored with 15 minutes remaining to decide the game, as Kolarov played all 90 minutes.
Elsewhere, Stephan El Shaarawy came on in injury time as Italy moved on to the play-offs with a closing 1-0 win over Albania.
Antonio Candreva grabbed the only goal of the game, with the Azzurri now waiting for next week's draw to see who they must beat for a place in Russia.
There was also a substitute appearance for Primavera defender Lirim Kastrati, who made his full international debut for Kosovo during their 2-0 defeat against Iceland.
The 18-year-old played 12 minutes in Reykjavik, as the hosts clinched their World Cup spot.
Cengiz Under, Roma's other player in action on Monday night, remained an unused substitute as Turkey drew 2-2 with Finland.
Results elsewhere on the night mean Edin Dzeko's World Cup hopes are unfortunately now over, with Bosnia & Herzegovina unable to secure a play-off spot even if they finish second in Group H.
Greece (Kostas Manolas), currently in pole position for that berth, will make the play-offs as long as they gain a better result than Bosnia & Herzegovina on Tuesday night.
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