The Steelmen led at the break after a fine volley from John Sutton but the Scottish champions improved after the break and Kris Commons secured a point for the home side when he converted from the penalty spot.
Motherwell took the lead on 19 minutes when Sutton got in front of his marker at the front post to volley home Josh Law’s cross from the edge of the six-yard box.
Sutton missed a golden opportunity to double the visitors’ advantage minutes later when he side-footed Keith Lasley’s cross wide from four yards out.
Deila introduced Commons and captain Scott Brown at half-time in place of Aleksandar Tonev and Beram Kayal as he looked to lift his team.
Those substitutions gave the Scottish champions the boost they needed and it was Commons who equalised from the penalty spot on 68 minutes after Brown was fouled by Craig Reid as he surged into the box.
Celtic turned the screw on Motherwell in the closing minutes but were unable to snatch a winner and almost conceded themselves when Zaine Francis-Angol squandered a late chance for the visitors.