The 22-year-old joined the French side on loan for the rest of the season having struggled for game time at Spurs since his summer switch from Middlesbrough.
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However, he made a crucial error in just his third appearance for Rennes. The right-back failed to clear a long ball up the pitch which allowed Bohdan Mykhaylichenko to run free into the box.
His shot was saved by Rennes goalkeeper Steve Mandanda, but 22-year-old Dmytro Kryskiv fired in the rebound.
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Shakhtar went on to claim a 2-1 win against their French opponents in the first leg of their Europa League knockout round play-off tie.
The Ukrainian side are one step closer to the last-16 and have so far been able to do well without their former star man Mykhailo Mudryk.
Mudryk left the club in January to sign for Chelsea, having been heavily linked with a move to Arsenal beforehand.
He joined the Blues in an £88million deal, with the 22-year-old being one of football's most exciting young talents.
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However, he is yet to find the back of the net for his new club, with Mudryk so far struggling to adapt to life in the Premier League.
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Spence on the other hand will be hoping to have a better second half of the season with Rennes.
All of his appearances for the side so far have been defeats, with his two previous games coming in Ligue 1.
His performances in the rest of the campaign could determine his long-term future at Spurs, who have an obligation to buy Pedro Porro in the summer.