In a game in which all three goals came from the penalty spot, the visitors, later reduced to 10-men following the 82nd minute dismissal of Zigor Aranalde for a second bookable offence went ahead on 18 minutes.
Chris Lumsdon scored from the spot at the second time of asking when his initial kick was saved by Shrews' teenage goalkeeping sensation Joe Hart, only for the referee to spot an infringement and he made no mistake the second time around.
But just after the half hour, the home side were level when Colin McMenamin netted with a spot-kick after he himself had been fouled.
The game was then ultimately decided 16 minutes from time with the afternoon's third penalty, and Shrews skipper Kevin Sharp clinched victory for his side after substitute Kelvin Langmead had been sent sprawling in the box.
After successive victories to start 2006, Shrews went into the match in a confident mood, as did second in the table Carlisle, who arrived at Gay Meadow seeking their seventh away win of the campaign.
This highly entertaining encounter burst into life on 17 minutes when Hart upended Karl Hawley as he closed in on goal. Referee Hill deemed a yellow card for the England Under-18 international sufficient punishment.
Hart then parried Lumsdon's first kick to safety, only for the ref to order a re-take, judging Hart to have moved before the kick was taken.
At the second attempt, Lumsdon then opened the scoring, but in the 32nd minute Town drew level. McMenamin picked himself up to score his eighth goal of the season from the spot after being fouled by Paul Armison.
Around the hour mark both sides went close to taking the lead, Hart saving smartly from Hawley with Shrews midfielder Jamie Tolley firing over at the other end.
But the issue was finally settled 16 minutes from time. Langley, who had replaced Glynn Hurst only five minutes before, was brought down by Peter Murphy, with Sharp stepping up to secure a fine win with a coolly struck penalty.