Murphy finished well in the 82nd minute to break Hibernian’s resilient response to Liam Miller’s 32nd-minute dismissal.
Motherwell dominated even before Miller was penalised for a late tackle on Jim O’Brien but Hibs deprived them of clear-cut chances until good forward play from John Sutton set up Murphy.
The win took Motherwell five points off third-placed Hibs and extended their unbeaten SPL run to eight games.
Hibernian manager John Hughes made five changes following the 5-1 thrashing by St Johnstone on Wednesday with goalkeeper Graeme Smith and Derek Riordan among those dropped.
Murphy was a replacement for Lukas Jutkiewicz after Motherwell’s top scorer suffered a knee injury.
Hibs also had a man sent off at Perth with the resulting suspension depriving Hughes of striker Colin Nish, whose physical presence may well have been utilised on poor Fir Park pitch, parts of which cut up badly even in the opening minutes.
Sutton saw a powerful 20-yard strike saved after a scrappy start and Motherwell began to play some decent passing football.
O’Brien volleyed wide before Graham Stack pushed the ball away after Murphy had diverted Giles Coke’s 20-yard effort.
The hosts kept the pressure on but Hibernian had the best first half chance after Stephen Craigan was penalised for a pass back at the end of a dangerous Hibs break.
Anthony Stokes lashed well over from 10 yards after the indirect free-kick.
The match exploded into life when Miller caught O’Brien on the ankle with a hard and late tackle, prompting his former Celtic team-mate into an angry reaction.
Miller was shown a straight red card by Euan Norris while O’Brien received a yellow for pushing the Hibs midfielder in the chest.
Motherwell were unable to exploit their advantage before the break and John Ruddy made his first save after Alan Gow worked space to shoot.
Motherwell pushed Hibs back after the restart and Murphy shot over after a low near-post cross by Tom Hateley before Sutton headed into Stack’s hands after another cross from the full-back.
Stack fumbled Sutton’s header wide following a cross by substitute Chris Humphrey as Hibs continued to frustrate their hosts.
Motherwell came closer in the 75th minute when Keith Lasley hooked the ball over Stack after Patrick Cregg had failed to clear Murphy’s deflected shot but David Wotherspoon got back in ample time to clear.
Hughes brought on the attacking threat of Merouane Zemmama but Motherwell’s pressure soon paid off.
Sutton held off Sol Bamba to lay O’Brien’s cross into the path of Murphy, who cushioned a volley just inside the far post from eight yards.
Hibs pushed forward but Ruddy ensured his seventh clean sheet in eight SPL games when he held Chris Hogg’s effort from a Zemmama corner, and Murphy and O’Brien came close on the break.