Racing are bidding to become the first French club to win the trophy since RC Toulon in 2015 and the three-time champions of Europe are themselves going for glory this evening (21.00 local time), when they take on Bristol Bears with the aim of adding the Challenge Cup to their collection of honours.
After first-half tries for Exeter by Luke Cowan-Dickie, Sam Simmonds and Harry Williams, a try by another England worldwide - Henry Slade - ultimately proved to be the key score after the center intercepted a pass from Scotland flyhalf Finn Russell.
No wonder director of rugby Baxter, a central figure in Exeter's rise, having made more than 300 appearances for the club, told reporters: "My emotions are all over the place, really".
"It kind of wasn't an Exeter Chiefs type of game, yet we ended up winning it".
"In some ways it was some of our poorest attack and poorest defence of the season".
Joining Beale among the substitutes is Donnacha Ryan, who is surprisingly kept in reserve after playing a key role in the hard-fought win over Saracens in the semi-final. "It is great for this group of players".
Ireland global full-back Simon Zebo touched down twice for Racing, while wing Juan Imhoff and hooker Camille Chat also crossed, with Maxime Machenaud adding a penalty and conversion and fly-half Finn Russell one conversion.
"We have been together a long time - my whole career - and she has seen the highs and lows".
"To start with she was just screaming at me in emotional joy, and then we managed to have a few words and talked about the journey and it was a nice few minutes".
The Chiefs, who can complete a domestic and European double with victory in next week's Premiership final, surged into a 14-0 lead only for Racing to pull back to within a point with 15 minutes to go.
Baxter told BT Sport: "It was a awful game to watch, and that last 14 minutes went on forever, but we have seen it out and it looks like it was meant to be".
"I won't worry about the elusive double right now".