Did you find any confirmation? My google search confirmed your memory of that Connors-Tanner match. It must have been 41 years ago: 1977 WCT challenge Cup in Vegas:
http://www.stevegtennis.com/draw-results/atp/WCT_Challenge_Cup/1977/
It went indeed 5 sets but none of the sets resulted in TB, so your remarkable memory got confused on that part. I found no record of RR matches in that tourney though
The other match of those 2 champs featuring all TB sets happened in 1981 Masters in NY, confirmed by ATP, but it was 3 sets only (won by Tanner) second last in their H2H:
https://www.atpworldtour.com/en/players/fedex-head-2-head/jimmy-connors-vs-roscoe-tanner/C044/T006
But you don't have to go that far back in time to find an unusual YE championship result, where a player with miserable 1-2 record in RR advanced and went all the way. Look at
Singapore 2015 (fresh enough so that even I can remember it) where Radwanska very luckily advanced out of a 3-way tie at the second place (by virtue of 3-4 in sets, while opponents were 2-4) and she went on to win the title with 2 very tough matches. So, even better than Tanner in 1977 because she won all the way!
Then, are you ready for that... the perfectly identical run from a poor 1-2 (and 3-4 sets) 3-way tie into the championship, was repeated in
Singapore 2016, this time by Cibulkova. Comparing said Singapore RR group standings from 2015 & 2016 and the two champions' paths, one may think this is some kind of sorcery: how could the WTA finals history repeat itself so literally?