Daley and Murphy both converted crosses to put Stuart McCall’s men well in command before the half-hour mark.
Murphy then appeared to glance home Daley’s strike midway through the second half as Motherwell emphatically opened up a seven-point lead in third place in the SPL.
Motherwell’s victory, their seventh away from home in the SPL this season, was a direct reversal of their only defeat to non-Old Firm opposition.
St Johnstone, who had taken seven points from their first three games under Lomas, were again without the injured Francisco Sandaza and Cillian Sheridan.
Marcus Haber and Carl Finnigan had deputised efficiently in victory at Tynecastle last weekend but Saints lacked a cutting edge.
Most of their chances came courtesy of Murray Davidson’s runs into the box and Motherwell goalkeeper Darren Randolph was relatively untroubled as his team-mates defended well throughout.
Both sides made two changes. David McCracken and David Robertson came in for St Johnstone with the injured Frazer Wright absent along with Kevin Moon.
Keith Lasley returned following injury for Motherwell along with Daley, with Stephen Hughes and Chris Humphrey brought on later on with the game already won.
Motherwell created the first chance after 70 seconds. Michael Higdon hooked a return pass to Nicky Law to take out McCracken but the midfielder sliced his shot well wide from the left channel.
Daley and Davidson saw low drives saved as both sides attacked in the early stages.
Motherwell began to control possession but Saints threatened when Liam Craig headed Chris Millar’s cross towards a crowded goalmouth, however Finnigan conceded a free-kick by handling the ball in the air and was fortunate to escape further punishment from referee Alan Muir.
Motherwell took the lead in the 16th minute as Daley claimed his second goal in three games. Neither goalkeeper Peter Enckelman or left-back Callum Davidson could deal with Law’s driven cross from the left and Daley had the simple task of tapping home from three yards.
The hosts almost replied instantly as Murray Davidson ran on to Craig’s cross but his header bounced just wide.
Motherwell doubled their lead in the 28th minute after capitalising on another cross. Daley was literally kicked off the park by Callum Davidson as he delivered from the right, but Muir’s decision to play advantage proved the correct one as Tom Hateley returned the half-cleared cross for Murphy to guide a free header into the bottom corner from eight yards.
Murray Davidson threw himself at Millar’s cross but the ball flashed wide and Saints had an escape just before the break.
Daley burst through the home defence and was brought down by Enckelman but Muir decided the goalkeeper had got the ball and gave a corner.
St Johnstone showed little sign of getting back into the game immediately after the break and Dave Mackay could not make the most of two chances to shoot from around the edge of the box.
Enckelman turned round Daley’s powerful strike after a counter-attack and Motherwell centre-backs Stephen Craigan and Shaun Hutchinson coped with an aerial onslaught before Motherwell went further ahead in the 68th minute.
Motherwell worked a short corner to Daley on the edge of the box and his powerful strike flashed in off a slight deflection that fooled Enckelman, with Murphy taking the credit.
Finnigan soon got in behind Craigan from Craig’s lofted pass but the striker did not look confident and sliced wide, and Motherwell were comfortable for the remaining 20 minutes.