Substitute Karlan Grant headed West Brom into the Carabao Cup second round as they edged Sheffield United 1-0 at The Hawthorns.
Grant's 73rd-minute effort - just three minutes after coming on - secured a tie at League One Derby in a game full of chances.
United, who made five changes from Saturday's 2-0 win against Millwall, could have been two goals up in the opening minutes.
Rhian Brewster drilled against the foot of the post and debutant Oliver Arblaster's follow-up was blocked by goalkeeper Alex Palmer, one of 10 Albion changes from Monday's 1-1 draw against Watford.