Evans was not originally selected for the tie, despite helping the British team win their last Davis Cup clash 3-2 against Slovakia in February.
No reason has been given for Baker's unavailability to face Russia, but Smith has said that Evans's previous form earned him a recall to the team.
"It was a really tough decision. I think all the players are pretty evenly balanced obviously outside Andy [Murray]," BBC Sport quotes Smith as saying.
"When I started thinking more when we got here about the court speed, the environment and also the match-ups against the Russians, it was my gut feeling that Dan had a slight edge over Jamie in these situations.
"Coupled with the fact that what Dan did last year in Davis Cup, when he really rose to the challenge and put in excellent performances against Slovakia and Belgium, is still fairly fresh in the memory."
Great Britain's match against Russia gets underway at the Ricoh Arena on Friday.