Alnwick did well to block an effort from Liam Davis in the 24th minute, smothering the 30-yard shot and keeping hold of the ball.
Stewart did manage to fire the visitors into the lead in the 37th minute, gaining possession inside his own half, bearing down on goal and beating Dunn with a low strike.
He turned provider as Charlton made it two on the stroke of half time, providing a cross for captain Johnnie Jackson to nod home in the 44th minute.
Yeovil almost hit back early in the second period when Miller's flick-on was struck towards goal by Joe Edwards, but his effort sailed over the crossbar.
Charlton came close to making it three in spectacular fashion just after the hour mark, with Simon Church's ambitious bicycle kick forcing a good save from Dunn.
The game opened up in the 72nd minute when Michael Morrison turned a cross into his own net to pull a goal back for Yeovil, and they had the chance to stage a comeback in the 75th minute when Andrew Hughes gave away a penalty.
Miller put away the resultant spot kick to send Huish Park into frenzy, but the atmosphere was soured somewhat when Jackson was shown a red card for a two-footed tackle.
Yeovil pressed for a winner in the dying stages, coming close when Miller curled a close-range effort wide, but Charlton held on for a share of the spoils.