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 bad light brought proceedings to a halt.
The players will return to complete the match on Saturday ahead of the doubles clash, which could mean than Murray has to play two five-set matches in one day.
Murray will be relieved to have come off, having complained many times during the match about the poor state of the clay playing surface.
Ward began in the ascendancy and took a 3-0 lead in the first set before his Italian opponent recovered to take it 6-4.
The second set went the way of the big hitting Brit before Fognini’s class shone through as he claimed the next two sets to give the Italians a 1-0 lead in their Davis Cup quarter-final.
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- Fabio Fognini