Englishman Sullivan started the day five shots clear at the top of the leaderboard but his advantage was cut to three as Otaegui carded five birdies on the front nine at Hanbury Manor Country Club in Ware.
Sullivan responded with a late flourish of his own, making four birdies on the back nine to finish 27-under and seven shots clear at the top.
It marks the 34-year-old's first European Tour victory since the Portugal Masters in 2015, the year of all his previous title triumphs.
Sullivan's sparkling form in 2015 earned him a place in the European team for the 2016 Ryder Cup, which the United States won 17-11.
Denmark's Rasmus Hojgaard finished third on 19-under with a bogey-free final round of 64.