Leeds Tykes suffer late anguish at fellow strugglers Tonbridge Juddians
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A last-minute penalty saw the home side edge ahead and win 29-27, leaving the Yorkshire side with a long trip home.
Tykes drew first blood with hooker Adam Brown touching down after three minutes, but Tonbridge ran in three tries to lead 21-5 at half-time.
Prop Ademakin Adebowale and left winger Harry Jukes scored tries early in the second half as the gap narrowed to 21-15.
Tonbridge scored another try to extend their lead to 26-15, but Leeds hit back to lead narrowly with tries from Will Hardwick and prop Dominic Hardman, a conversion from Venables giving them a 27-26 lead.
But a penalty in the final minute from Ryan Taylor-Dennehy gave Tonbridge the win.
As a result, Tonbridge remain bottom of the table on 29 points while the Tykes are a place better off on 41 points but with a game in hand on their rivals.
In National Two, Wharfedale led 12-0 after two tries from hooker Madison Hunting, but they went on to lose out 43-12 at Loughborough Students.
Otley are just one win away from securing the North Premier title after a 78-0 thrashing of bottom-of-the- table Northwich.
Two tries each from Elliot Morgan, Adam Malthouse and Struan Connor helped them to victory.
Elsewhere, York had to settle for two bonus points from a narrow 43-41 home loss to Lymm.
However, Sandal were 30-12 winners over Wirral with Dan Fawcett and James Ellar scoring two tries each.
Driffield were 25-20 winners over Pocklington as they clung on to top spot in North One East with one game to go, although second-placed Ilkley are level on points and have two games left to overhaul their rivals.
Ilkley beat visitors Durham City 54-10, while Cleckheaton remain third following a 40-19 win over Malton and Norton.