The Baggies played for more than an hour with ten men after striker Rob Hulse was given a red card for a rash challenge on Burnley defender Mark McGregor.
Albion manager Gary Megson thought the sending off was harsh but his opposite number Stan Ternent reckoned it was be valid and thought Andy Johnson was somewhat fortunate to escape a red card for a challenge on Tony Grant.
Burnley looked to be heading for victory when Blake accepted a pass from Glen Little before turning smartly to curl a shot across Russell Hoult and into the far bottom corner.
A defensive blunder, Burnley playing offside in error, led to Horsfield bursting clear top score a stunning equaliser.
It was the striker's second goal in two games and only the upright and a great block by former West Brom keeper Brian Jensen denied Horsfield a hat-trick.
The Clarets had more of the ball in the second half but Albion, even with Horsfield on his own up front, looked the more menacing and could easily have snatched a famous victory.
That said, Burnley were unlucky not to win it in stoppage time when Hoult pulled off a brilliant save to deny Blake.