Jim Bentley's men had been peerless in League Two heading into the game, claiming a maximum 12 points from their opening four fixtures.
And that record looked set to continue when captain Mark Hughes found the net with a header six minutes before half-time.
Cole Stockton, who signed a new three-year contract with Tranmere this week, repaid that faith by pulling his side level - taking the ball around goalkeeper Barry Roche before smashing past defenders on the line.
Hughes' afternoon took a turn for the worse when he was sent off for an off-the-ball incident involving Kayode Odejayi, before Stockton scored again for the home side by finding the net from a Matt Hill cross in the last minute.
That defeat for Morecambe opened the door for both Burton Albion and Cheltenham Town to overtake them at the summit.
Koby Arthur struck in the 90th minute to earn Cheltenham a 1-0 win over Hartlepool United, while Burton - boosted by a midweek victory over Premier League outfit QPR in the League Cup - were 2-1 winners at Mansfield Town.
Robbie Weir was sent off for Burton late on after a confrontation with Ritchie Sutton.
Morecambe's winning run may have come to an end on Saturday, but York City continue to cling on to one of this season's more bizarre records.
Nigel Worthington's men came into this weekend having drawn all four of their matches in the league, and they were at it again as they were held to a goalless draw by Wycombe Wanderers.
It is the first time since the 2001-02 season a team have drawn their opening five Football League fixtures.
Oxford United pushed West Brom all the way in the cup on Tuesday - eventually losing out on penalties - but they are in trouble at the foot of the table after claiming a share of the spoils in a six-goal thriller against Dagenham and Redbridge for their first point of the season.
That point lifted them above Accrington Stanley on goal difference, with James Beattie's side beaten 2-1 at 10-man Bury, having initially taken the lead in the 19th minute.
Shrewsbury Town maintained their unbeaten run with a 2-0 home win over Luton Town, who also had a man sent off, while Portsmouth lost for the first time this season at home to Newport County.
Carlisle United looked some way short of being able to pick up their first win in League Two as they were thumped 5-0 at Cambridge United, and Exeter City are still winless following their 1-0 defeat at Northampton Town.
Elsewhere, Stevenage claimed a 3-2 win at AFC Wimbledon, and Plymouth Argyle beat 10-man Southend United 2-0.
