Robson was injured as she and Heather Watson both won their singles matches before Britain lost the dead doubles rubber in Eilat.
Robson was out of sorts in the opening set against a player ranked 93 places below her at 138 in the world but she came back to triumph 0-6, 6-2, 6-1 against Greta Arn.
However, the 19-year-old had to call on the trainer for treatment to an injury to her left shoulder at the end of the first set, something which will be of concern to captain Judy Murray ahead of today's showdown.
Robson said: "After the first set I thought, 'this can't get any worse'. I regrouped and played better in the second and third sets."
Watson had things much more her own way as she won 6-3, 6-2, over Timea Babos, who needed treatment for a back problem during their match.
Watson said: "I'm really pleased I played better today, especially mentally.
"I got off to a good start and even when she got back to 3-3 I kept up the pressure and the second [set] was easier.
"I'm very proud that we're through to tomorrow's play-offs."
Robson and Johanna Konta were unable to complete a whitewash as they lost 6-4, 2-6, 6-2 to Reca-Luca Jani and Katalin Marosi in the doubles to leave the final match score 2-1 to Britain.
Bulgaria enjoyed a comfortable 3-0 win over Slovenia in a tie which also saw a player compromised by injury.
Dia Evitimova won 6-1, 6-0 against Tina Rupert before Slovenia's Tjasa Srimpf retired after losing the first game of her match against Tsvetana Pironkova.
Elitsa Kostova and Isabella Shinikova were 6-2, 6-3 winners over Andreja Klepac and Rupert in the doubles to complete the whitewash.
The winner of today's match will earn a World Group II play-off in April, which could be Britain's first home tie for 20 years.