The Reds were a goal behind at the break after a poor first-half, which saw very few goalscoring opportunities in a bitterly cold afternoon.
John Yems reacted by bringing on an extra forward in Tom Nichols, who replaced the quiet Tyler Frost.
The hosts immediately improved and found a leveller just minutes after the restart. James Tilley followed up his goal at Barrow last week, with a stunning strike from outside the box.
Crawley’s tails were up and it looked like they then might find a winner but it was Mansfield who broke clear and sealed the three points.
Here’s how we rated the players.
1. Glenn Morris - 7
Didn't have to make a huge number of saves but his goal was breached twice. Hard to argue that he could have saved either, though. He otherwise did his job when called upon.
Photo: Steve Robards
2. Archie Davies - 7
Got in good positions going forward. Had a golden chance to play in Appiah one-on-one but he couldn't beat the defender. Good defensive headers as Crawley had to withstand heavy pressure early on. Put in pleny of crosses to no avial as Crawley fought to get back in the game for a second time.
3. George Francomb - 6
Showed some good link-up play as he looked to progress with the ball but was caught out in defence a few times. A tame effort straight at the keeper in injury-time.
4. Tony Craig - 6
A strong start, with a couple of crunching challenges, which were hard but fair. Couldn't prevent opener but put in another good tackle on Rhys Oates as bared down on goal, looking to extend the visitors' lead. Needed treatment after taking a hit to the face. Would have stung more in the cold weather. Would have been grateful to see a shot go over the bar in the second half, which came from his defensive error.