The match was finished on Saturday after their rubber was halted by bad light on Friday.
Having won the opening set, Murray had just saved a series of set points to keep the score at 5-5 in the second when proceedings were brought to a halt.
Murray broke Seppi almost immediately as play resumed on Saturday to take the second set 7-5.
Credit to Seppi, though, he broke early in the third to take the advantage as the Brit began the set hesitantly but Murray secured two breaks in quick succession to take a 5-3 advantage.
Seppi was broken again as he served to stay in the match as Murray won in straight sets to level the tie with the doubles to come later on Saturday.
Murray had struggled with the court at times and speaking after the win said: "The court's pretty dangerous, I hope no-one gets hurt this weekend."
"For the most part the court is ok. There are a few bad bounces, but that back corner is not good enough. It is dangerous," he continued
"If this was on the tour they would not be using this court, that is something we will talk about after the tie because the last thing you want is for people to be injured. It doesn't need to be like that."
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