Eaton reached the second round at Wimbledon last year
Chris Eaton maintained his bid for a GB Davis Cup spot against Ukraine by beating James Ward 6-3 6-2 6-7 (3-7) 2-6 21-19 in an epic play-off.
Eaton's win took six hours, 40 minutes, which, had the match been sanctioned by the ATP Tour, would have made it the longest in history by seven minutes.
Favourite Josh Goodall maintained his 100% record with a hardfought 6-3 3-6 7-5 4-6 6-2 win over Alex Slabinsky.
Colin Fleming caused an upset by defeating Dan Evans 7-5 6-2 0-6 6-0.
Great Britain captain John Lloyd introduced the six-man play-off to select two players for his squad ahead of next weekend's tie.
Only a player winning all three of his matches will be certain of a place in the team. Eaton and Goodall are the only unbeaten players so far.
Great Britain play Ukraine in the second round of the Davis Cup's Europe/Africa section in the Braehead Arena in Renfrewshire from 6 to 8 March.
Speaking from the Dubai Championships, Andy Murray said he thought the play-offs were a good idea.
"The players have very little experience of playing five sets and it is a good opportunity to see how fit they are and if they are ready to play three five-set matches in three days," he told BBC Sport.
"By the sound of these results there were some very long matches. The guys will be tired but that is what they need going into the Davis Cup."
Murray has been struggling with an ankle injury and sounded a note of caution for Lloyd when asked if he would be fit for the final stages in Dubai, followed by the Davis Cup.
"I'd love to be fit for both but if it's too sore to play I'll have to make the right decision," he said.