The Croat, then 18, upset Federer in the first round on his Wimbledon debut in 2002, since when the Swiss has won 64 consecutive matches on grass, 39 at the London grand slam where he has lifted the trophy five times in a row.
World number one Federer, in devastating form from the start, allowed Ancic only one point in his first four service games as he ran away with the opening set.
Ancic improved after a rain delay lasting two hours and 13 minutes with the score 1-1 in the second set, playing a full part in some high quality rallies.
Games went with serve until the 11th when the 1.95-metre tall Croat netted a volley to give his opponent the break point.
Federer was in full flow in the third set and won the match in one hour and 41 minutes on his first match point, going into a semi-final against Russia's Marat Safin.
When play resumed after the rain delay Ancic immediately looked like he had benefited with a marked improvement in his game.
But Federer still took the only break when Ancic netted a volley to go to deuce then double faulted to hand the Swiss the point.
A great rally was won by Ancic in the next game but Federer then hit three service winners in a row followed by an ace to take the set.
Ancic, at 24 two years younger than Federer, won a 16-minute game at the start of the third set which went to deuce 10 times and in which he fended off four break points.
He was less successful four games later when Federer continued to apply his slide-rule tennis, finding the lines and corners with consummate ease, and converted the first break point to go 3-2 up.
Federer set himself up with three match points but needed only one, hitting a second serve as though it was a first straight down the middle at 112 mph for an ace.
After that defeat by Ancic in 2002, Federer has now beaten the Croatian in all six of their subsequent meetings.
