Evans, egged on in Sydney by his captain and idol Tim Henman, survived a late charge by the Belgium star, who saved five match points in the Group C tie before succumbing 6-4, 6-4.
“It was real tough out there but my coach told me it was never going to be easy,” said Evans, who has climbed to 42 in the world after starting last season at 199.
“The guys on the bench were just saying ‘next point, next point’. I was nervous as well, no doubting that, but really proud of my efforts to come through like that.
“He’s a world class player and his quality started to show towards the end,” added Evans, who made the final at Delray Beach last week.
It was a disappointing defeat for Belgium’s top player, who won his first match of the season on Friday against Moldova’s Radu Albot and said he had big ambitions for the 2020 season.
Britain claimed the tie 2-1 when Jamie Murray and Joe Salisbury won the deciding doubles after Cameron Norrie lost in two sets to Belgium’s Steve Darcis.
Former world number three Dimitrov whipped Albot 6-2, 6-3 on Sunday to help Bulgaria clinch their second tie in a row and put them in a commanding position in the group. He beat Evans in their opening clash on Friday.
The majority of teams at the 24-nation event have standalone skippers, mostly leading former players such as Boris Becker and Marat Safin.
But the Bulgarians chose to bestow the honour on Dimitrov and he has thrived in guiding his inexperienced team.
“My dad was the one who taught me how to play tennis, and when I was chosen to be a captain, he was, like, ‘Oh, now you’re going to see what is it to be on the other end’,” said Dimitrov, who slipped down the rankings last year after a shoulder problem.
“And I really did and I am. But I’m enjoying it. I never thought I could do the whole double role, but I took this on board.
“I wanted to give something back to the boys and just make sure that they learn. That’s it. That’s all I want, to kind of give whatever I can from me to them. So I think things are good so far.”
Dimitar Kuzmanov gave Bulgaria a winning start by overcoming Alexander Cozbinov 6-1, 7-5 before Dimitrov returned to play doubles with Alexandar Lazarov, falling to Albot and Cozbinov in two sets.
“I know I have to not only believe in myself now but I need to believe in the players that are with me,” said Dimitrov.
“My only goal was, and I’m honest on that, was just to put them together, to make sure we practise together, to make sure they learn something from me.”