A controversial penalty decision left Carlisle with just a point to show from a game they appeared to have under control until substitute Paul Mullin tumbled to the floor and Padraig Amond sent Hanford the wrong way from the spot.
The United players protested the decision, as Grainger emerged from his tussle with Mullin, but the referee was unmoved as he pointed to the spot and waved the complaints away.
Carlisle built well down the left flank as Dempsey and Brough exchanged passes early on and a deep cross from Corry, as he called for it, had to be dealt with as Wyke steamed in.
Morecambe responded with a slick move of their own as Devitt overlapped to get to the byline. His low cross fizzed across the face of goal but Redshaw couldn't quite get there.
Both sides wanted to attack and Dempsey took matters into his own hands when he surged forward. He let one fly as he reached the edge of the box and Ward had to go full length to palm it behin.
A scramble followed from the dipping corner but Rigg was stopped in his tracks, just four yards out, as Wyke was penalised for a tug on Hughes.
Wyke and Rigg combined with a one-two as United kept the pressure on and a run of early corners kept the visitors on their toes as Dempsey and Corry found good deliveries. A downward header from Wyke was deflected behind by Hughes from one such swirling ball and the defender was relieved to see it shave the outside of his post.
Potts thundered a rasping volley just past the angle of post and bar but Morecambe showed they were still in the game when an accurate pass left Redshaw with space to attack. His shot was blocked as it appeared to be heading for the bottom corner.
The Shrimps enjoyed a good spell as the game settled into a pleasing pattern of passing football but they couldn't open the door as the Carlisle defence soaked up the high and low balls into the box.
Morecambe almost struck on the counter attack when a block tackle on Dempsey found Redshaw with options in midfield. He took it forward and Devitt stepped in to take over as Grainger tried to crowd them out. He threaded a shot through a tight gap but it was always heading wide.
Potts drilled another long range effort wide of the target as he arrived late from deep, and Ellison had to be watched as he burst through at pace from a reverse pass from Redshaw. Archibald-Henville was there to make sure the door was closed.
It was a stuttering start to the second half as both sides wasted opportunities to make their possession count, but Brad Potts made his third shot from distance of the day count when he left Ward flapping at thin air from a half cleared Dempsey free kick. He seemed to take everyone by surprise when he pulled the trigger and sent it expertly into the bottom corner.
Wildig went close when he drilled a shot through legs as Morecambe tried to reply, but he could only find the side netting as Hanford made the dive.
Midfielder Potts missed the chance to double his tally for the day when Wyke put it on a plate but his shot, from 12 yards and from the angle, was hit on the rise and continued the theme from there.
Substitute Billy Paynter almost made an immediate impact but his volley was well dealt with by Hughes when he made a block. Hanford gathered it well at the other end when Kenyon struck a 40 yarder at the centre of the goal, but he had to pick the ball out of the back of the net with 13 minutes left to play when Mullin was barged to the floor by Grainger. Padraig Amond placed the ball on the spot and sent the stopper the wrong way as he wheeled away to celebrate.
Redshaw rattled the bar with a rasping dipper as the Shrimps went in search of a second, and Ellison had to be marshalled as he spun and shot on the edge of the box.
A late cross-shot from Kennedy was a whisker away from being touched in by Paynter as Carlisle tried to nick the win, but the feeling of the day was disappointment as the final whistle blew on a game the Blues had appeared to have sewn up and in the bag.
United - Potts (53)
Morecambe - Amond (78 pen)
United - Wyke (81)
Morecambe - Redshaw (19)
Carlisle United - Hanford, Young, Archibald-Henville, Grainger, Brough, Potts (Kearns 83), Kennedy, Corry, Dempsey, Rigg (Paynter 68), Wyke (Asamoah 83). Subs - Spiegel, Buddle, Thirlwell, Griffith.
Morecambe - Ward, Beeley, Devitt (Mullin 73), Kenyon, Hughes, Edwards, Redshaw, Ellison, Wildig (Fleming 66), Wilson, Parrish (Amond 59). Subs - Stewart, Wright, Goodall, McGowan.
Referee - Mr Peter Bankes
Attendance - 4,343 (383 away fans)