Top seed Federer, who will now face former world number one Marat Safin for a place in the final, moved into an impressive 17th consecutive Grand Slam semifinal, a run stretching back over four years.
Ancic, a former top 10 player who is still feeling his way back after battling glandular fever and injury, was the last man to beat Federer on grass here in 2002 -- but has lost their last six matches.
"I played great today. I served excellently with many aces which is always important against a player like Mario," said Federer who fired down 15 aces on his way to victory.
"It was a tough day. There was a rain delay which broke my momentum a little bit because I had started really well but I got back into it and played really well. It's a privilege to be in another semifinal and I'm looking forward to the challenge."
Federer, now with 64 wins in a row on grass, stormed through the first set in just 20 minutes breaking the 24-year-old Croatian in the second and sixth games and giving up just a single point in four service games.
At 6-1 and 1-1 in the second set, rain forced the players off Centre Court for over two hours but on the resumption, Ancic briefly rediscovered his composure.
However, a poor volley followed by a second double fault of the match on break point in the 11th game gave Federer a 6-5 lead which the champion converted into a two-set lead with a ninth ace after only 56 minutes on court.
A marathon opening game of the third set, which lasted 16 minutes, went in Ancic's favor before Federer again broke, this time in the fifth game for a 3-2 lead.
Ancic, a semifinalist in 2004 and who spent almost four hours coming back from a two-set deficit to beat Fernando Verdasco in the last round, was visibly wilting and Federer swept to victory courtesy of his 15th ace after only one hour 42 minutes of action.
Meanwhile, unseeded Safin continued his remarkable run in this year's tournament by recovering from the loss of the opening set to defeat 31st seed Feliciano Lopez.
Safin, world ranked 75 but a winner of two Grand Slam titles, became the first Russian to reach the semifinals in the Open era after going through 3-6 7-5 7-6 6-2.
The 28-year-old looked in danger of imploding when he was given a warning for ball abuse and dropped the first set, but he kept his cool to brush aside his Spanish opponent and set up a clash with Federer -- who he beat en route to winning the 2005 Australian Open title.
"I was too nervous to play good tennis at the beginning and had to calm down," Safin said. "I started a bit nervous because I had never beaten him in a big tournament and he's a very difficult player who was full of confidence, but I got a lucky break and that made a difference.
"I want to believe I'm back. I have gone up a few steps in the rankings, back in the top 50, which is great. No matter what I do against Roger it has been a great two weeks."
Safin destroyed world number three Novak Djokovic in the second round and, playing with renewed confidence after that victory, he has now swept aside three more seeds.
CNN
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