The outcome looked settled with Muguruza earning a comfortable 3-0 lead early in the tiebreak, before saving two set points to earn three match points of her own.
After winning the opening set, a frenetic second that featured four breaks appeared poised to go the way of Wimbledon champion Muguruza, who saw off two Kasatkina set points in the tie-break, only to see the Russian hold firm and deny her at 8-7, 9-8 and 10-9.
Defending champion Elina Svitolina needed more than two hours to overcome Qiang Wang 6-1, 5-7, 6-2 Wednesday and reach the quarterfinals of the Dubai Championships.
"I didn't expect [to play three sets], but I always try to expect unexpected", Svitolina said after the match.
But the momentum switched as Osaka gradually found her serve and began to hit her groundstrokes with more confidence, pace and accuracy.
"It should be a good final, Daria is playing well, and she's won some tough matches". "Very hard match. I think she always plays very good against the top players". But I was very happy with the way I was playing.
Daria Kasatkina caused a huge shock in the evening under the lights of Centre Court as she ousted world number three Garbiñe Muguruza in three thrilling sets, triumphing 3-6, 7-6, 6-1 having outstandingly saved three match points in the process. "We were both giving our best and we were fighting the end - it was set point, then match point, it was up and down", said Vesnina. "I had to be ready for her to raise her level".
On Kasatkina, she added: "She plays well, she had tough matches".
In yesterday's first doubles semi-final, Taiwan's Chan Hao-ching and Yang Zhaoxuan of China defeated Alicja Rosolska of Poland and Abigail Spears of the United States 6-4, 7-5 in 1 hour, 29 minutes to advance to today's final.
Muguruza came into the tournament on the back of an excellent performance at the Qatar Open, where she lost a thrilling final to Petra Kvitova.