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Andy Reid curled over from 25 yards soon after, before Hull created a gilt-edged opportunity from close range.
In first-half stoppage time Boyd made no mistake from close range to give Hull the lead against the club for whom he nearly signed for just two months ago.
Forest responded strongly after the break and were level through Darius Henderson, who reacted quickest to tuck home a composed rebound after Cox's shot crashed back off the crossbar.
Billy Sharp was sent on soon after for the visitors, who went close to taking the lead when Henderson sent a header wide despite being unmarked at the far post.
Brady curled a strike wide as Hull came back into the match before Stephen Quinn had a low effort well saved by Darlow.
Both sides chased a late winner but Forest got the crucial goal when substitute Lewis McGugan's low strike squirmed under Stockdale to make it six successive away wins for Davies.