Chasing 169 to win, Sathish stood tall amid the ruins with a 38-ball cameo that comprised six boundaries.
Sathish came into bat when the score was 118 for six, needing 71 runs for Tamil Nadu to reach the last four.
The man of the match did not get the needed support from Baba Indrajith (48), Ravichandran Ashwin (7) and Aswin Crist (4), who failed to get into the double figures, towards the end of the chase. TN play Gujarat in the semifinals on Saturday.
India discard pacer Praveen Kumar tasted the first blood by removing Karthik and then Bhuvaneshwar Kumar sent back Mukund, Aparajith and Balaji in a jiffy.
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Nevertheless, Vijay Shankar (22) and inform India opener Murali Vijay (33) stabilised the innings and brought Tamil Nadu close to sniffing distance of the victory target.
Both put on 64-run partnership for the fifth wicket before Vijay was trapped leg before by Saurabh Kumar.
Later, Sathish stitched a vital 37 and 35 run stand for sixth and eighth wicket partnership with Indrajith and Ashwin, making the difference in the end. Which will played on December 26.
Opting to bat, Uttar Pradesh posted 168 all out in 48.2 overs with Rinku Singh being the top scorer with a 97-ball 60 runs.
Uttar Pradesh too suffered a bad start as half of the team was back in the pavillion with the score reading 41.
Piyush Chawla was the second highest scorer (29) and seven other batsmen could not reach double digits.
Balaji was the most successful bowler for Tamil Nadu, who scalped Shubham Chaubey (6), Saurabh Kumar (3) and Akshdeep Nath (13).