The 26-year-old made his fifth start for the club since moving to the Indian Super League club from Bidvest Wits at the end of last season.
After Kolkata fell behind to a Raphael Augusto goal after 28 minutes, Doutie bagged an important goal right on the stroke of half-time to pull his side level.
Doutie then turned provider once again – as he was in their 3-2 win over Kerala Blasters last week – as he set up Canadian striker Iain Hume to score the winning goal in the 63rd minute.
Kolkata are second on the ISL table after 11 games, one point behind Goa.