Ancic, seeded fourth and making his return to tennis this week after a summer swimming injury, hung on against persistent fifth seed Dominik Hrbaty, seeing off the Slovak for a 2-6, 7-6 (7/4), 6-4 victory.
But favourite Ljubicic was upended by eighth-seeded Korean Hyung-taik Lee in a 6-3, 7-6 (7/3) knockout.
The Asian outsider also won the pair's only other match two years ago at the US Open.
The 30-year-old winner came good as he competed in his third quarter-final of the season, moving into a second semi-finals in the Chinese capital.
Lee, standing 60 spots below world No. 3 Ljubicic, established early superiority with a break in the first set which the Croatian could never get back.
With the seed struggling, Lee seized his opportunities taking the second set into a tiebreaker after back-to-back breaks.
Ancic will now get a chance to avenge the loss of his Davis Cup teammate as he faces Lee in Saturday's semi-final.
“It was an extremely tough match,” said Ancic of his win over Hrbaty.
“Every time we play, it's close. I felt on the defensive and was not able to exactly play my game.
“But in the end, I found enough rhythm to win.”In the bottom of the draw, Russian second seed and US Open semi-finalist Nikolay Davydenko returned from a day trip to the summer palace in time to face Thai sixth seed Paradorn Srichaphan later.
The winner of that match will clash with either third-seeded Australian Open finalist Marcos Baghdatis or Thailand's Danai Udomchoke.
Results (quarter-finals): Mario Ancic (CRO x4) bt Dominik Hrbaty (SVK x5) 2-6, 7-6 (7/4), 6-4; Hyung-taik Lee (KOR x8) bt Ivan Ljubicic (CRO x1) 6-3, 7-6 (7/3); Marcos Baghdatis (CYP x3) bt Danai Udomchoke (THA) 6-2, 6-1; Paradorn Srichaphan (THA x6) bt Nikolay Davydenko (RUS x2) 6-2, 1-0, retired.
DAVENPORT ADVANCES
BALI: Defending champion Lindsay Davenport crushed Czech Hana Sromova 6-1, 6-0 at the Wismilak International tennis tournament on Friday, setting the stage for a semi-final showdown with top-seeded Svetlana Kuznetsova.
''She's very dangerous and I'm excited to play,'' Davenport said of her upcoming face-off with the Russian, who advanced in straight sets Friday with a 6-3, 6-2 win over France's Severine Bremond.
''I need to serve well to win ... If she sees a lot of second serves and is able to dictate play with her forehand it's going to be a tough day for me.''
In the other semi-final, Switzerland's Patty Schnyder will play Marion Bartoli of France. Schnyder won a battle of two left-handers, dismissing Hungarian Melinda Czink 6-2, 6-2, while Bartoli ousted Russia's Olga Poutchkova 6-2, 6-4.
Davenport was never in trouble against Sromova.
''It was great,'' said the third-seeded American. ''There wasn't much more I could have done. She hits a very different ball, not a lot of rhythm and she plays some funky slices and doesn't have a lot of pace, but I thought I played well and overpowered her.''
But Davenport is prepared for a tough battle against Kuznetsova, a two-time former champion who has never lost a match in her three trips to Bali.
Kuznetsova had to wait until her sixth break point of the match before taking a 3-1 lead against Bremond, and then promptly dropped her own serve. But the Russian broke again for 5-3 and held off two break points to take the set.
Kuznetsova also needed six break points before taking a 1-0 lead in the second set, and Bremond double-faulted to leave her serving for the match at 5-2.
''I was trying to do too much with the ball,'' Kuznetsova said of her struggle to win break points. ''If I played simpler I would win easier, but this is what I want to improve in my game, to do more things.''
Results (quarter-finals): 2-Patty Schnyder (Switzerland) beat Melinda Czink (Hungary) 6-2 6-2; 6-Marion Bartoli (France) beat Olga Poutchkova (Russia) 6-2 6-4; 3-Lindsay Davenport (U.S.) beat Hana Sromova (Czech Republic) 6-1 6-0; 1-Svetlana Kuznetsova (Russia) beat 8-Severine Bremond (France) 6-3 6-2.—Agencies