Ross County 2 Hamilton 1
Thomas Mikkelsen ended Ross County's wait for a home win as his late goal saw off Hamilton.
The Danish forward calmly stroked in a pass from fellow substitute Alex Schalk to seal a come-from-behind 2-1 win.
Schalk pulled County level on 71 minutes to cancel out Greg Docherty's opener at the start of the second half.
It ends a run of six home games without a win and gives Coyle his first triumph in Dingwall.
The Staggies made one change from the 2-1 defeat to Hearts, bringing in Billy McKay for Ross Draper. Accies dropped Giannis Skondras and Massimo Donati for Darren Lyon and Steven Boyd.
County were on the lookout for their first home win of the season, something which chairman Roy MacGregor and boss Owen Coyle have put a premium on. They had a promising opening, with Jason Naismith fizzing a ball across the face of goal that Davis Keillor-Dunn was unable to turn in.
Shortly after they were in again, Michael Gardyne setting McKay racing clear on 17 minutes, only for Alex Gogic to recover and intervene before the Northern Ireland international could get a shot away.
McKay has had a slow start to his County career, coming to Dingwall on the back of a groin operation, and was still looking for his first goal. The ex-Caley Thistle striker must have thought he had opened his account on 24 minutes, leaping to flick a Naismith cross goalwards, but Ryan Fulton clawed it away.
For most of the first half only the Staggies looked like threatening and Keillor-Dunn was proving a useful outlet. The 19-year-old, who has aspirations of representing Scotland's under-21 side, race clear of Gogic and centred, with the ball reaching Naismith at the back post who smashed into the stanchion behind the goal.
Both teams traded chances through Gogic and Naismith at the start of the second period, before Accies' tactic of landing corners right in Scott Fox's goalmouth finally worked.
The majority had been negated due to fouls on Fox but they got one right on 53 minutes, with Boyd picking out Docherty to plant a header home from six yards.
County huffed and puffed but were not testing Fulton enough, with Coyle switching both his strikers without adjusting the side's system.
But one of those substitutes proved effective as Schalk levelled the scores with his first touch, heading in Naismith's cross with 19 minutes to go.
They looked tired at the back County and were affording Hamilton space. Antonio Rojano's cross picked out an unmarked Dougie Imrie at the back post, who sliced his volley into the side netting.
Michael Gardyne had a late opportunity to decide the game from Kenny van der Weg's centre but Mikkelsen was the hero, keeping pace with Schalk on the counter then rolling his square ball past Fulton for the win.