Mauresmo is scheduled to meet fifth seed Svetlana Kuznetsova of Russia in the last eight.
"I was crying because it was a very emotional moment, " said Mauresmo after beating Shaughnessy.
France led 2-0 lead after Saturday, with Mauresmo beating Lisa Raymond and Mary Pierce overcoming Shaughnessy.
Injury has consistently hampered Mauresmo's efforts to become a regular challenger at Grand Slams.
In the early matches, fifth-seeded Amelie Mauresmo eliminated Russian Tatiana Panova in straight sets 6-4 6-3.
Mauresmo played with heavy strapping on both thighs as she battled past Hantuchova in three sets.
Mauresmo and Nathalie Dechy are paired against Vera Douchevina and Dinara Safina in Sunday's doubles.
In Sunday's reverse singles, Pierce will face Myskina, while Mauresmo will take on Dementieva.
Second seed Amelie Mauresmo of France faces a tough opener against 1994 Wimbledon champion Conchita Martinez of Spain.
Former world number one Amelie Mauresmo was among a host of players to voice their support for Peer.
But in the second singles match, world number four Mauresmo hit back to beat Anastasia Myskina 6-4 6-2.
Williams has won the Paris title twice, beating former world No. 1 Amelie Mauresmo in the final both times.
She follows the likes of Amelie Mauresmo, Martina Hingis and Tracy Austin as a winner of the junior singles title.
If her fragile confidence has taken a battering in Shanghai, names like Venus, Capriati, Hingis and Mauresmo could do further damage.
Mauresmo, Australian Open finalist two years ago, is long overdue a good run on a surface to which her game is suited.
"It became very hard in build-up to the US Open, " said Mauresmo, who won the silver medal at the 2004 Olympics in Athens.
Second seed Amelie Mauresmo of France beat Tathiana Garbin 6-2 6-1 and US Open champion Svetlana Kuznetsova defeated Czech Eva Birnerova 6-3 6-2.
Mauresmo eased past Shaughnessy 6-2 6-1 to give France an unassailable lead in Moscow and they went on to wrap up a 4-1 victory.
Sharapova and Amelie Mauresmo, who just started consulting for Azarenka, each won almost 80% of their matches in the year after reaching No. 1.
French second seed Amelie Mauresmo overcame stubborn Russian fifth seed Svetlana Kuznetsova 7-6 4-6 6-2 and plays Australia's Alicia Molik for the other final place.
"I'm not surprised she's got this far, " Mauresmo said of Molik.
"It's tight, just like we knew it would be, " said Mauresmo.
Kim Clijsters produced a magificent third-set comeback to pip fifth seed Amelie Mauresmo 3-6 6-3 7-5 and gain a place in the Porsche Tennis Grand Prix final.
The Russian top seed, still seeking her first Grand Slam title after falling to Kuznetsova in the Paris final, will next play 2006 Wimbledon champion Amelie Mauresmo.
World number one Serena Williams pulled out with a knee injury ahead of Saturday's semi-final against Dementieva, before Mauresmo beat second seed Jelena Jankovic in the second semi.
Dementieva eventually secured a 6-7 (5-7) 6-1 6-4 victory over Safarova to go one better than last year when she lost to home hope and now retired Amelie Mauresmo.
The Australian beat Mauresmo 7-5 3-6 6-3 in the second round in the San Diego tour event three weeks ago after losing to her in the Australian Open in January.
Mauresmo failed to win any of four game points at 5-5, as Clijsters, who came from a set behind to been second seed Lindsay Davenport in the quarter-finals, again broke.
Mauresmo held serve for the first time and then had three break points on the Safina serve - converting the last of them to get right back into the contest.
应用推荐