Harris’ display meant Smith’s decision to give Draper, 22, more time to recover paid off, but he could return for the round-robin contests against Argentina and Canada later this week.
Britain are aiming to finish in Group D’s top two and reach the Davis Cup Finals last eight in Malaga this November.
Evans and Neal Skupski could not complete a clean sweep as they fell to a 7-6 (7-4) 7-5 doubles defeat against Virtanen and Harri Heliovaara.
Britain could be left to rue not winning the tie 3-0, with the competition’s format meaning every match counts until the end.
“It feels disappointing because it is a long day and last year [at the same event] it almost came back to bite us, not getting that 3-0 on the first day,” added Smith.
“But it is a positive day. At the start, when you don’t have Jack and Cameron Norrie – your two highest ranked players – and end up winning a tie 2-1, you’d take that.”
