Murphy was 5-3 behind going into the evening session but started with a 137 break and never looked back, winning four straight frames.
The pair shared a series of tactical frames at the end of the session which left Murphy in control.
However Hendry's maximum break was the highlight of the day's play.
The Scot, 40, has now had nine maximums in his career, including one other in Sheffield in the 1995 semi-finals.
Providing no-one matches it, Hendry will earn £147,000 for the maximum and £10,000 for the highest break.
Frame seven's last black glanced both jaws before dropping into the pocket to the delight of the Crucible crowd.
After sinking a tricky pink with his penultimate shot, Hendry was left with an awkward cut back into the bottom corner to complete the clearance.
An anxious moment followed as the black briefly threatened to squirm free, before the crowd stood to acclaim the veteran.
The chance of a 147 came when a cannon off his fifth black opened up the pack and a pair of plant shots squeezed home to put the maximum within reach.
"It's a tremendous feeling and I'm absolutely delighted," said Hendry, who lost the last frame of the session to lead the best-of-25 match 5-3.
It is the ninth maximum in the history of the competition with Ronnie O'Sullivan and Ali Carter both achieving the feat last year.
Cliff Thorburn, Jimmy White and Mark Williams are the only other players to clinch perfect frames at the sport's greatest tournament.
"You have to grade maximums at the Crucible as the best because of the pressure of this venue," six-time champion Steve Davis told BBC Sport.
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