Despite being untroubled during the first period, Josh Griffiths could do nothing to prevent Wrexham from netting following the restart. Windass finished off a quick move 90 seconds into the second 45, getting the visitors back within one.
They then equalised around the hour mark. Dobson flicked home for 2-2 – and suddenly it was game-on at The Hawthorns.
Albion’s biggest opportunity to win came in the final stages, substitute Daryl Dike’s close-range attempt was somehow saved, while Griffiths was also then on hand to deny Kieffer Moore’s late shot.
Ultimately, neither team found a winner and the clash ended level.
Albion: Griffiths, Imray, Phillips, Campbell, Styles, Jimoh-Aloba (Taylor 72), Molumby, Diakite, Price, Heggebø, Maja (Dike 72).
Substitutes: O’Leary, Gilchrist, Mowatt, Whitwell, Bostock, Mustapha, Sule.
Attendance: 25,927 (2,522).