The visitors put some good early pressure on the Airdrie goal and eventually got their reward on 16 minutes when a Simon Donnelly cut-back from the byline found Mark Roberts, who fired the ball into the roof of the net.
Airdrie almost got back on level terms minutes later when Kevin McDonald broke from midfield and fired a shot from 25 yards, only to see Arthur tip the ball around the post.
The home side were controlling the game at this stage and pushing hard for the equaliser.
It almost came on 27 minutes when Xavier Barrau played Stephen McDougall through on goal, but again Arthur was on hand to turn the shot over the bar.
Airdrie did get back on level terms on 37 minutes when the ball fell to Stuart Taylor following a scramble in the goalmouth, and his shot into the ground bounced over the helpless Arthur and into the net.
Then, just before half-time, Airdrie should have taken the lead when the ball broke to McDonald just inside the box but his shot went inches past the post.
Thistle again took the lead early in the second-half when Derek Young charged down the right flank before squaring for Adam Strachan who turned the ball in.
Airdrie piled on the pressure in search of an equaliser but were denied by two superb saves from Arthur, firstly to deny Taylor then Bryan Prunty.