Luke Garbutt’s superb freekick gave Town the lead but Stefan Payne equalised for Tranmere to leave the scoreline 1-1 at half-time.
The Blues made three changes to the team which won 1-0 at Gillingham last week with Luke Woolfenden dropping out of the back three and on the bench and Cole Skuse moving back from midfield between skipper Luke Chambers and James Wilson. Garbutt returned at left wing-back with Gwion Edwards among the subs.
Jon Nolan came back into the central midfield three alongside Flynn Downes with Alan Judge ahead of them - with Andre Dozzell moving to the bench - behind front two James Norwood, facing his old club, and Kayden Jackson.
After a scruffy start, Tranmere came close to carving out the game’s first opportunity in the 13th minute when Paul Mullin almost played in Payne, however, his pass was too far in front of the ex-Shrewsbury striker and Blues keeper Tomas Holy claimed.
Within a minute Alan Judge - as at Gillingham last week given free rein to roam - found himself space on the left of the box and his cross was eventually half-cleared to Downes, who scuffed a half-volley well wide.
The visitors had the ball in the net in the 18th minute but referee Ben Toner having adjudged that Payne had handled the ball into the path of Neil Danns before the former Colchester man’s shot beat Holy.
On 21 Judge was sent flying by a very clumsy Emmanuel Monthe challenge on halfway with the defender lucky not to be booked.
From the freekick, Downes played the ball to the Irishman, who turned a looping ball into the box towards Chambers, who claimed he was fouled by Monthe but referee Toner waved away the skipper’s protests.
Oliver Banks shot high and wide for Rovers in the 26th minute with Town still to really get going after an untidy and often ponderous first third of the match.
Chambers headed wide at the far post from a Skuse freekick on the right in the 29th minute, then at the other end Payne laid the ball back to Mullin on the edge of the box but the ex-Morecambe man scuffed weakly towards goal under pressure from Downes, illegally he claimed but to no response from the referee.
Danns curled a shot wide from distance as Tranmere continued to look the more dangerous of the two sides with the Blues a long way from their best.
Darren Potter was shown the first yellow card of the game in the 34th minute for a foul on Judge as the Blues sought to break on halfway.
And from that freekick the Blues won another a few yards outside the area from which Garbutt gave them the lead.
The on-loan Everton man struck as sweet a left-foot strike as you’ll see into the top left-hand corner of Tranmere keeper Scott Davies’s net giving the Rovers skipper no chance.
Garbutt ran away towards the East of England Co-op Stand to celebrate the best of his three goals in four starts for the Blues.
But Town’s lead - and their record of clean sheets - wouldn’t last too long. Mullin seized on a Chambers error and brought it forward and inside from the left before playing wide to Jake Caprice on the right. The wing-back sent a low ball across the edge of the six-yard box, Holy failed to claim and Payne touched it over the line for his fourth goal of the season.
It was a poor goal to end Town’s run of clean sheets, which would have stretched to a club record six if they had failed to concede today, and curtail their total minutes without conceding at 539.
Neither side was able to threaten again before referee Toner ended the half with the scoreline a fair reflection of a disappointing period for the Blues.
Town, with Skuse having moved into midfield before the end of the half, had rarely been in control of the game and had created nothing prior to Garbutt’s brilliant Beckham-esque freekick.
The Blues’ lead was harsh on Tranmere who had been better on the ball than Town and had created the game’s few openings. Their equaliser summed up the Blues’ scruffy half, probably their poorest 45 minutes of the season so far.
Paul Lambert’s men need to be much better after the break if they’re to continue their winning run.
Town: Holy, Chambers (c), Skuse, Wilson, Vincent-Young, Downes, Nolan, Judge, Garbutt, Jackson, Norwood. Subs: Norris, Edwards, Rowe, Dozzell, Woolfenden, Georgiou, Huws.
Tranmere: Davies, Caprice, Nelson, Monthe, Ridehalgh, Banks, Morris, Potter, Danns, Mullin, Payne. Subs: Pilling, Hepburn-Murphy, Jennings, Ponticelli, Gilmour, Blackett-Taylor, Walker-Rice. Referee: Ben Toner (Lancashire).