The Serbian international was unfortunate once again shortly after the break when he dug the ball out from under hit feet and chipped Jaaskelainen from the edge of the area, but it clipped the top of the crossbar.
Henman had four opportunities to secure the match, but Agassi dug deep, forcing a tie-break and eventually pipping Henman to secure the match 7-5 1-6 7-6 (12-10) in a thrilling finale.
Stephens did not make the best possible start as Williams went one set and a break of serve ahead, before the 19-year-old American dug deep to pull out an unlikely triumph.