Davies opened the scoring with a drilled effort that went in off the post, following a pinpoint pass from Diego Fagundez.
Moments later, Portland almost got back on terms after Diego Chara's shot from distance came back off the frame of the goal.
Just after the half-time interval, Diego Valeri squandered a golden chance to equalise when the forward found himself one-on-one with Bobby Shuttleworth, but he tried to loft the ball over the keeper and his effort drifted wide.
However, the Timbers did find a leveller through ex-Aston Villa defender Ridgewell, with just over a quarter of the game left.
The hosts had Shuttleworth to thank for preserving parity, as the stopper produced a tidy save from point-blank range to prevent Maximiliano Urruti from firing Portland ahead on 82 minutes.
Caleb Porter's side would not fashion a better chance to snatch the points as both team shared the spoils.