Daly was prominent in the Gers attack and could have added a second, but he failed to convert his opportunities.
Aird went close to doubling their advantage midway through the first period when his thunderous strike came back off the crossbar, with Wood beaten in the Arboath goal.
The champions were on the back foot after the interval when Paul Sheerin twice went close to an equaliser for the hosts.
Rangers almost got back in front within moments of the restart when Aird chested the ball down for Daly, but the striker skied his effort under pressure.
With Ally McCoist's side in danger of losing their perfect record on the road, it fell to substitute Calum Gallacher to help save their blushes. With three minutes remaining, he played in Aird and the midfielder tucked the ball home.