The Ammies made them work hard for the points, dominating the first half hour and leading through Matty Lund's ninth minute opener.
But, after Jordan Bowery had seen a finish cleared off the line, Stags went in 2-1 up after Stephen McLaughlin set up Rhys Oates before netting a cheeky free kick just before half-time.
Salford increasingy had more of the ball in the second half but Mansfield defended stoutly and keeper Nathan Bishop had little to do as Stags continue to climb the table.
Mansfield made three changes, two of them enforced at the back where centre halves John-Joe O'Toole (illness) and Will Forrester (injury) missed out.
They were replaced by Farrend Rawson and Oli Hawkins, who was back from illness.
The other change saw midfielder Harry Charsley drop to the bench to be replaced by lone striker Oates, who had recovered from injury.
Elliott Hewitt moved over to form a back three with Hawkins and Rawson with Bowery at right wing back.
On a bitterly cold afternoon, the game had only just entered its second minute when Quinn was hurt by a Turnbull tackle and needed treatment.
Stags weathered some City pressure before some quick passes saw Bowery send a dangerous cross through everyone on six minutes.
But Salford continued to probe and were ahead on nine minutes.
Love hurled in a long throw from near the right corner flag, Elliott flicked it on at the near post and Lund was on hand to turn the ball home low from six yards.
On 15 minutes Lapslie released Oates into space on the left of the box, but his left-footed effort could only find the sidenetting.
Quinn was hurt for a second time after a tackle from behind by Lowe on 18 minutes which earned the City man a booking.
The resulting free kick found Bowery, who lashed wide of the near post.
Two minutes later Hawkins was added to the book for his challenge on McAleny.
It was proving hard work for Mansfield, but they almost levelled on 23 minutes.
McLaughlin sent in a deep cross from the left which Bowery directed on target on the volley and beat King only to see Vassel head heroically off the line.
Salford resumed their offensive and McAleny shot straight at Bishop on 24 minutes and two minutes later, with Hawkins alongside him, tried to squeeze the ball past Bishop from a tight angle.
But the finish did not have enough legs to cross the line and Hewitt was able to clear.
Mansfield were on level terms on 36 minutes from a free kick just to the left of the box.
McLaughlin drilled it hard and low into the six yard box where minimal contact from Oates guided it over the line.
McLaughlin then put Stags ahead from another free kick on 45 minutes.
From 25 yards out and on the left of the box, he shaped up to cross but then caught the keeper out with a low shot inside the near post.
Stags ended the half well on top, forcing two successive corners.
Salford survived an early second half scramble as King pounced on a loose ball before Bowery could reach it.
On 50 minutes Maris fed Bowery on the right and he came inside onto his left foot and curled a finish inches wide of the far post as Mansfield began the second half far stronger than the first.
On the hour Bowery drew huge applause for a neat turn and powerful finish into the sideneting.
Lapslie's foul on Turnbull on 69 minutes saw the game's third caution as the home side were pressed back into their own half for long periods but defended comfortably.
Sinclair took over from Oates for the last eight minutes.
With two minutes left Elliott headed over from a long cross and before play restarted Quinn was replaced by Charsley.
Four minutes were added on but Stags were in no mood to let go of three more precious points.
STAGS: Bishop, Hewitt, Rawson, Hawkins, McLaughlin, Maris, Stirk, Quinn (Charsley 88), Lapslie, Oates (Sinclair 82), Bowery. SUBS NOT USED: Shelvey, Nartey, Burke, Law, Gale.
SALFORD: King, Love, Touray, Lowe, Eastham, Lund, Elliott, Morris (Oteh 82), Turnbull, McAleny (Shephard 57), Vassell (Wright 82). SUBS NOT USED: Jeacock, Golden, Smith, Dackers.
REFEREE: Anthony Backhouse
ATTENDANCE: 4,113 (73 away).