Freeman, on loan from Arsenal, was at the heart of Boro's dominance but failed to find a way past the equally impressive Walker in the Walsall goal.
The 19-year-old striker let fly either side of the break and laid on chances for Chuks Aneke and Scott Laird, but the Saddlers stood firm to escape with a share of the spoils.
Stevenage should have scored from their opening attack but Laird lashed Luke Freeman's corner over the bar, before Arsenal loanee Freeman's 12th-minute strike forced Walker into a fine save.
Boro dominated the first half but, after fellow on-loan Gunner Aneke volleyed narrowly over, Adam Chambers almost punished their wastefulness when he pounced on a loose ball and Chris Day did well to save.
Freeman won a free-kick which Michael Bostwick fired narrowly wide before the young striker again struck the palms of Walker, but it was Walsall who wasted the best chance to win it when Jon Macken blazed over from eight yards.