The sixth-seeded British No 1 now has a fantastic chance of making the final as he is the only seed left in his side of the draw.
Henman raced into a 4-0 lead and although Tillstrom held his next two service games, the British No 1 sealed the first set 6-2. In the second set, Henman broke again to move into a commanding position and, at 5-3 down, Tillstrom was serving to stay in the match.
Henman forced the game to deuce and then produced two stunning passes to take the match 6-2, 6-3 and set up a quarter-final showdown with Spain's Francisco Clavet today.
Henman said: "This was definitely an improvement on my last match over Sergi Bruguera. It was not startling, but it was better. If I wanted to be picky, there were a few too many unforced errors. But I was moving the ball a round well."
He added: "This is a good opportunity. The draw has opened up from top to bottom. But everyone still left in is a good player, each has his strengths.
"Against Clavet, I'll be the one trying to dictate play, as he will be staying on the baseline. But I will have to be aggressive and control the points and be patient."
Another player Henman will not have to deal with his the second seed, Marcelo Rios, of Chile, who fell to the Czech Republic's Martin Damm. Rios, No 6 in the world, was carrying a thigh injury and lost 4-6, 7-5, 7-6.
The Brazilian Gustavo Kuerten, ranked 83rd in the world, took advantage of a blistering serve and Andre Agassi's tender ankle to defeat the former world No 1 6-4, 6-2 in 65 minutes at the St Jude tournament in Memphis yesterday.
The fourth-seeded Wimbledon runner-up, MaliVai Washington, also slowed by an injury he suffered in winning a Davis Cup singles match against Brazil, lost 7-6, 6-3 to the 108th-ranked Argentinian, Javier Frana.