But their cause was not helped as West Hartlepool won and Malton and Norton ended a seven-game losing streak by beating second-placed Morpeth.
Dinnington made the better start against Driffield and a break from a lineout brought a penalty that Chris Williams kicked to put the home side ahead after three minutes.
The lead was short-lived as Driffield levelled from a penalty.
The visitors quickly went on to the attack again but were bundled into touch inside the home 22 and were then held up over the line after they had earned a scrum at a lineout.
Dinnington cleared, but Driffield came back before again being forced into touch.
Eventually, Dinnington managed to get out of their half and midway through the period a break by Jonny West was carried on by Ollie Rodgers, who selflessly off-loaded for Matt Shaw to score in the corner for an 8-3 lead.
Williams kicked a penalty to stretch the home lead, but Driffield finished the half strongly and a try and two penalties saw them turn the game on its head to lead 16-11.
In the final minute of the half, however, Dinnington kicked a penalty to the corner, worked the ball through several phases from the lineout and Tom Doughty scored under the posts. Williams added the conversion to give Dinnington a two-point lead at half-time.
Driffield had the benefit of the elements in the second half, forcing the home side to spend most of the period in their own 22.
Resolute defending prevented the visitors adding to their points total, however, and from their first attack of the half Dinnington won a penalty that was kicked to the corner.
That set up a catch-and-drive, giving Garry Woodcock a try, which Williams converted to move Dinnington more than one score ahead.
Dinnington continued to defend well and looked dangerous when they had the ball in hand.
Midway through the half the hosts stole the ball and won a penalty, but the kick at goal was missed.
A minute later they chose to kick another penalty to the corner but lost the ball in the tackle.
In the final ten minutes Driffield got on top and looked for a losing bonus point.
But two quickly-taken penalties were knocked on and a final attack turned over.