The visitors fought back from Kane Hemming's early goal to level and hit the woodwork as home anxiety grew.
Even after Rose had sent the stadium wild with his 12th goal of the season, the home side were forced into backs to the wall defending in the five added minutes.
This was a real Christmas cracker of a match with a host of chances at both ends and Morecambe heading north wondering how they didn't get a point as relieved Stags won a League Two game for the first time in four and also scored for the first time in three.
Stags should have been out of sight by half-time but then had to weather a superb Morecambe fightback in which they scored and hit the post.
But Stags got the win they so desperately needed at the death.
There was a big boost for Mansfield as striker Hemmings was passed fit to play after shaking off his calf injury.
His return was one of four changes as boss Steve Evans reverted to a 4-4-2. Joining Hemmings in the side were midfielders Butcher, Digby and Hamilton.
Out went Angol, Pearce, Atkinson and Mellis – all dropping down to the bench.
Mansfield began the game well, but it was Morecambe who had the first goal attempt on three minutes after Digby gave the ball away.
Campbell ran on and saw Benning block his first shot before pulling his follow-up low and wide.
A minute later Hamilton volleyed into the Morecambe sidenetting at the far post after a long White cross reached him from the right.
Stags had a double let-off on 16 minutes.
Campbell fed the overlapping Conlan in space to his left and his finish was superbly saved by Logan.
From the corner Lavelle was left unmarked in acres of space, but Logan was down well to block his header.
Stags went straight upfield to snatch a eighth minute lead.
Rose got the flick-on from a long, high forward ball and Hemmings raced on down the middle, confidently beating the advancing Roche inside the left post.
Kenyon was well over from a speculative 25 yard snapshot for the visitors on 13 minutes.
Stags might have done better on a 26th minute breakaway.
Rose fed Hemmings who delayed a shot and instead set up Hamilton. But he took too long getting a shot away and his eventual finish was woefully wide.
A minute from the break another chance went begging for the home side as Diamond threw himself at a MacDonald free kick from the left but sent his diving header wide.
Less than a minute after the restart Morecambe skipper Rose let fly from 25 yards and wasn't too far wide.
But the visitors were level on 50 minutes. From a throw on the right, Campbell gave the ball to Lang in the box and, given too much time, he was able to drill a low shot from a tight angle across goal and inside the far post.
Stung, the home side made a double change on 54 minutes.
Mellis and Anderson were sent on in place of Hemmings and the ineffective Butcher.
The home fans were furious to see Hemmings go, having had an excellent first half, with the manager roundly booed from the stands.
The decision may also have been down to his fitness levels, with Hemmings only just coming back from injury, but the boos rang out just the same.
Hamilton saw the game's first booking on 59 minutes for sliding into a late challenge on Muller.
Rose again tried from distance for the visitors and again it wasn't far off in the 61stminute.
Morecambe were growing in confidence and the home crowd more impatient and on 66 minutes only the post saved the Stags as Campbell shot from 25 yards and the ball clipped the woodwork.
Shortly after MacDonald crossed from the left and Rose flicked a header wide at the far post.
Mansfield's final change came on 70 minutes as Digby, who had created little, was replaced by Atkinson.
Morecambe continued to shoot on sight as Rose whistled another just wide from distance.
Mellis tried the same for Stags and was also wide.
On 77 minutes Rose floated a cross in from the left and McGurk's on-target header required a save from Logan.
It then took a crucial block by White to prevent sub Ellison volleying in a far post cross.
Hamilton drew applause for a good run down the left which ended with a powerful shot inches over with 10 minutes remaining.
Ellison drew his customary booking at Stags on 87 minutes for bringing down White.
The stadium then exploded into joy and relief as Rose restored Mansfield's lead with two minutes to go.
Anderson floated in a superb far post cross from the right and Rose jumped well to head home at the far post.
Home fans were hoping Ellison may be shown a red after a clash with White on the touchline, but it ended only with a yellow for White.
In the last of five added minutes Rose went down as he tried to go past Roche. The striker was booked for the dive and the keeper booked for his continued dissent.
In a thrilling grandstand finish Lavelle twice came close to levelling as Bennett headed off the line and seconds later Logan was down to make a save from his second attempt.
STAGS: Logan; White, Bennett, Diamond, Benning; MacDonald, Butcher (Mellis 54), Digby (Atkinson 70), Hamilton; Rose, Hemmings (Anderson 54). Subs: Olejnik, Pearce, Angol, Spencer.
MORECAMBE: Roche, McGowan, Kenyon, Old, Oliver (Ellison 72), Campbell (Thompson 81), Conlan, Lavelle, Muller, Rose, Lang (McGurk 72). Subs: Nizic, Fleming, Lund, Osbourne.
REFEREE: Ross Joyce of Teeside.
ATTENDANCE: 3,058 (63 away).
CHAD STAGS MAN OF THE MATCH: Conrad Logan.