The two sides are battling relegation and Tigers were leading with about 15 minutes to go with a try from Ed Simmons and some accurate kicking from Mark Ireland.
But Harrogate’s Sam Fox had kept them in the game, slotting over penalties.
The try from Coser and the resulting conversion from Fox saw Harrogate hit the front and they managed to hold on for the win.
Wharfedale let victory slip from their grasp in the last few minutes of their game against South Leicester, losing 21-20 in a game they needed to win.
Two penalties and two conversions from Jamie Dale, as well as a penalty try and an Adam Howard effort had given Wharfedale the lead, only for South Leicester to win with a penalty in the dying stages of the contest.
Leading 27-24 early in the second half, plucky Otley were beaten 52-27 by league leaders Caldy.
A Blackheath try and conversion ten minutes from the end saw Hull Ionians lose 31-29 away from home in National One.
An Isaac Green penalty and Phil Eggleshaw try had given Ionians an 8-0 lead before two tries and a conversion from the home side saw Blackheath take a 17-15 lead at the break.
Sam Wilson and Zac Poole crashed over after the restart to put Hull 29-24 up, with Poole’s effort ensuring a bonus point.
But they couldn’t hold on as Blackheath scored late on, although Ionians left with two bonus points for their tally.
Cleckheaton were left to rue missed chances as they lost out 19-17 at home to promotion chasing Rossendale.
Winger Josh Hall scored the only try of the first half as Cleck led 5-0 at half-time, but had missed the conversion and hit the crossbar with a penalty attempt.
After Rossendale had taken the lead with a converted try, winger Ollie Depledge re-took the lead with a try in the corner, before Rossendale went back in front at 14-10.
Richard Piper’s 60th-minute try was converted by Ronan Evans as Cleck took a 17-14 lead, but a late pushover try from Rossendale proved decisive, as a 40-metre penalty attempt from the hosts went wide and was the last play of the match.
Morley ran in five tries to secure a five-point win over Yorkshire rivals Sandal, emerging 29-18 winners from their National Three North fixture.
Elsewhere, Ilkley lost 19-8 at Kendal.
Trailing 19-10 at half-time, Sheffield hit back to win 26-19 at Longton in National Three Midlands.
Prop Toby Ademakin scored two tries in the first half, while after the break No 8 Jonny France also scored twice with Steve Depledge and Andy Hodgson both kicking penalties.
Down to 13 men as the whistle approached, Sheffield had to endure a sustained onslaught from Longton to seal the win.
Winger Mark Calderwood scored both tries for West Leeds as they took a 21-15 win at Keighley in Yorkshire One.
The rest of the points came from two different kickers with Stefan James converting a penalty and a conversion before dislocating his shoulder. Kier Breakwell stepped up to kick two second-half penalties to close out the game.
Heath battled to a 16-14 win over Old Brodleians, with winger Luke Saltonstall scoring a try and Esra Hinchcliffe kicking the conversion, two penalties and a dramatic drop-goal in the final minute to seal a thrilling win.
Pontefract progressed to the quarter-finals of the Yorkshire Shield with a 29-19 win against Old Rishworthians.
Their three tries came from inside centre Matt Bacon and wingers Stewart Sanderson and Richard Dedicote.
Liam Kay kicked the rest of their points and they will battle Wetherby for a place in the last four.