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Bale played a Wales record of 111 games for his country and was a five-time Champions League winner with Real Madrid.
Timothy Weah's 36th-minute goal was cancelled out by Bale's 82nd-minute penalty.
They edged Ukraine 1-0 with the solitary goal scored in the first half.
Aaron Ramsey and Connor Roberts scored in a 2-0 win over Turkey in their second Group A match.
Bale has joined Spurs on a season-long loan deal and although the financial details of the move were not disclosed, British media reported that Tottenham will pay around 20 million pounds in wages and loan fees.
Bale has won four Champions League titles since joining Madrid from Tottenham Hotspur in 2013 for a then world record 100 million euros.
The French legend clarified that it was the club who wanted to sell the Welsh forward, not him personally.
The victory means Zinedine Zidane's side move to the top of the table, for a few hours at least, before Barcelona play later on Saturday at home to Real Mallorca.
Bale has a long and successful record playing at Villarreal, scoring there on his Real debut in 2013 after completing his 100 million-euro move from Tottenham Hotspur and netting in a 3-2 win in 2017 and a 2-2 draw in 2018.
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