The striker’s deft header in the 69th minute created a 12-point lead over seventh-placed Aberdeen following the Dons’ lunchtime defeat by Hearts.
Murphy missed by far the best chance of a first half controlled by the hosts, but Kilmarnock improved before a controversial free-kick award allowed Tom Hateley to set up the Scotland Under-21 striker.
The victory further confirmed Motherwell as the SPL’s form team of 2010 as Craig Brown’s men kept their eighth clean sheet in nine unbeaten games since the turn of the year.
Motherwell had been warned in midweek that their “inadequate” pitch had to improve and a sizeable square in front of the dugouts was cordoned off during the warm-up following work to flatten and strengthen the ground.
The club received some positive pre-match feedback from the SPL’s pitch experts, although the worst affected area of the sandy surface cut up as the match progressed.
Motherwell lost Jim O’Brien to illness before the game but replacement Chris Humphrey made a lively start as the hosts forced a number of set-pieces.
Murphy caused problems with his pace and Manuel Pascali was forced into a risky shoulder charge on the striker after misjudging Keith Lasley’s searching ball, but Iain Brines dismissed penalty claims.
Two low crosses from Stevie Hammell caused concern in the Kilmarnock defence before being cleared and Cammy Bell comfortably held three long-range efforts from Well striker Lukas Jutkiewicz.
Kilmarnock emerged as an attacking force in the 26th minute when John Ruddy pushed wide Craig Bryson’s 25-yard volley and then touched over Kevin Kyle’s back-post header from Iain Flannigan’s corner.
Motherwell quickly regained control despite suffering a blow when Jutkiewicz suffered a recurrence of the knee injury that kept him out of the previous weekend’s victory over Hibernian, with Giles Coke coming on to fill his role just behind Murphy, who soon missed a great chance.
Pascali again lost a long ball, this time from Stephen Craigan, to leave Murphy clear on goal but Bell dived to his left to push away the youngster’s low measured effort.
James Fowler replaced Conor Sammon at half-time as Kilmarnock matched Motherwell’s 4-5-1 formation and both teams proceeded to cancel each other out.
Kilmarnock created the first opening of a tight start to the second half when Kyle laid the ball off for Bryson to shoot just over from 20 yards.
The visitors were looking far more comfortable but they were undone after Fowler was harshly penalised for a challenge on Coke on the left edge of the box.
Hateley swung in the free-kick and Murphy ran away from his marker to glance a header inside the far post.
Motherwell almost made it two when Coke broke down the left and fired a low shot across goal but Bell parried before Fowler cleared as John Sutton ran in.
Killie brought on Mehdi Taouil and Danny Invincibile as they threw men forward in a bid to extend their seven-match unbeaten run but Motherwell continued to look the more dangerous team.
Murphy had a shot saved after working space inside the box and then screwed badly wide after a one-two with the impressive Steve Jennings in a late counter-attack.