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Fourth-placed Ilkley travelled to face the second-bottom side without joint captain Ben Magee, who was on paternity leave.
Despite his absence, the visitors dominated possession during the opening 25 minutes.
Two consecutive penalties from Charles Morgan took Ilkley to within 20 metres.
The line-out was secured before the ball was moved to Louis Anderson, who crossed close to the posts and converted his own try to give the visitors a 7-0 lead.
Five minutes later, another penalty and line-out provided the platform for a second score.
Morgan found Kieran Wileyman with a long pass, and he beat the covering defence to touch down wide on the left.
Anderson's conversion drifted wide, but Ilkley led 12-0.
Driffield responded, however, and continued to compete even after Henry Furbank was shown a yellow card for a shoulder charge.
Ilkley conceded two penalties in quick succession, and with referee Tom Howard playing advantage, right wing Owen Scurry used a dummy to cross.
James Watts converted to bring the hosts back to 12-7.
Ilkley had a chance to restore their advantage with the final play of the half, but Anderson's penalty struck the post.
The visitors began the second period poorly, failing to deal with the kick-off, although Morgan made ground before an infringement at the breakdown allowed Driffield to clear.
Ilkley returned to the attack but struggled against the hosts' determined tackling once again.
Their task became harder when Jayden Marsters and Wileyman were both sent to the sin-bin in quick succession for high tackles.
Driffield took advantage, with scrum-half Joe Girking crossing for a try.
Watts missed the conversion, leaving the scores level.
Harry Smith and the Ilkley pack threatened in response, but Driffield held firm before launching a counter-attack.
Billy Nichol was then shown a third yellow card for the visitors after an offence at the breakdown, leaving Ilkley with just 12 players.
Despite their numerical disadvantage, the Dalesmen regained the lead against the run of play.
A Driffield attack broke down and Anderson gathered the loose ball, racing over unopposed beneath the posts.
He added the conversion to put Ilkley 19-12 ahead with less than 15 minutes remaining.
Driffield struck back three minutes later, with Finn Styche crossing for a try which Watts converted to make it 19-19.
The final 10 minutes saw possession swing between the sides, with Ilkley looking the more threatening.
Back to a full complement, they were awarded a penalty with three minutes remaining and Morgan kicked to within 10 metres of the line.
However, the line-out throw was deemed crooked, and Ilkley conceded a scrum.
Further frustration saw them penalised another 10 metres.
A final penalty gave the visitors one more opportunity, but they could not find a way through before Howard brought the contest to an end.
It was a draw that will feel like a missed opportunity for Ilkley.
Magee's absence was significant, but indiscipline proved costly, allowing Driffield back into a match the visitors had initially controlled.
Ilkley now turn their attention to this week's visit of Hull, who are finding form following relegation.
The Dalesmen will need greater discipline, but their performances at Stacks Field suggest they have the quality to claim a result.