In the early stages, Celtic failed to effectively deal with a short corner, allowing Howat space around the penalty spot to connect cleanly with the dropping ball and power a volley into the net.
Rangers almost doubled their advantage soon after when Wilkinson's edge-of-the-area strike forced Kelsey Daugherty into a spectacular save.
Moments later they thought they had made it 2-0 but Middag's celebrations were cut short as her headed goal was ruled out for offside.
Lucy Ashworth-Clifford threatened for Elena Sadiku's side after breaking in behind, but her dinked attempt from inside the area was easily gathered by Victoria Esson.
The Celtic forward then had an opportunity to level moments before the interval, but failed to get on the end of an inviting cross after some determined defending from Brogan Hay.
Both sides continued to have chances after the break but none were clear cut, until Emma Lawton was judged to have blocked a cross with her arm in the area, allowing Wilkinson the chance to add to her side's lead from the spot.
Lawton made amends for her mistake when Celtic ventured forward, winning her side a penalty at the other end, which Noonan showed composure to convert.
A late spell of Celtic pressure resulted in the ball falling for Barclais to strike back across goal and in off the post, sealing a late point for the visitors who had trailed for most of the game.