Fifth-placed Stanley, who will now face Stevenage in a two-legged showdown, fielded a virtual reserve team and trailed to Russell Penn's 46th-minute goal.
But boss John Coleman's second-half substitutions paid dividends as Winnard rescue a point six minutes from time to make it one defeat now in 19 for Accrington.
Both teams had a chance to break the deadlock in the 25th minute. Burton keeper Adam Legzdins did well to keep out an Alan Burton shot which sparked a swift Brewers break ending in Calvin Zola shooting tamely against the legs of Ian Dunbavin.
Burton went on to miss more gilt-edged chances before half-time, Greg Pearson firing wide with only Dunbavin to beat while defender Tom Parkes headed over a gaping goal. Yet the hosts needed only a minute of the second half to take the lead as midfielder Penn timed his run to head in Aaron Webster's cross from six yards.
Stanley had chances to level but Tom Smyth dragged a shot wide and substitute Andy Procter had a fierce effort punched to safety by Legzdins. But an improving Accrington were rewarded when Winnard stole onto the end of a Chris Turner free-kick to equalise from close range in the 84th minute.