Spain bids farewell to Hopman Cup on high note
However, Muguruza got the job done as she defeated Cornet, who also struggled with back discomfort, 6-1, 6-3 in one hour and 15 minutes to earn her first singles win, having lost to Australia's Ashleigh Barty and Germany's Angelique Kerber.
Then, her compatriot David Ferrer battled past Lucas Pouille 6-4, 6-7 (5-7), 7-6 (7-2) in two hours and 48 minutes to grab his second men's singles win after defeating Australia's Matt Ebden and losing to Germany's Alexander Zverev.
The French duo eased past Osuigwe-Ferrer 4-2, 4-2.
Spain wraps up the round-robin in the third spot with one win and two defeats, ahead of France who lost its three ties.
Australia and Germany are competing for a place in the final, scheduled for Saturday.
Switzerland, comprising Roger Federer and Belinda Bencic, has already booked its place in the championship match as Group B winners.
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