Charlie Wyke's 66th-minute volley looked to have been enough to give Carlisle the points, but two goals in as many minutes in injury time settled the game in Shrewsbury's favour.
First, Mickey Demetriou headed home the equaliser before James Collins struck in the fourth additional minute.
The result sees the Shropshire club leapfrog Burton Albion and Wycombe Wanderers at the summit. Burton were held to a 0-0 draw by AFC Wimbledon - who had defender Mark Phillips sent off - while Wycombe lost 2-0 at home to Plymouth Argyle.
A first-half double from Joe Pigott saw Southend United boost their promotion hopes with a 2-0 victory against Cheltenham Town, while Luton Town fought back to draw 2-2 with struggling York City in a game they played in part with nine men.
Josh Carson and Emile Sinclair put York in command, but the game turned on Jake Hyde's red card, with Luton then levelling matters thanks to a Mark Cullen double.
Luton had been reduced to 10 men when Nathan Doyle limped off after they had used their three substitutes, but he was forced to come back on and complete a dramatic game when Steve McNulty was sent off four minutes from time.
York also had Jake Hyde sent off as they let slip a two-goal lead.
Bottom club Hartlepool United aided their survival prospects by beating Northampton Town 1-0, but Mansfield Town slipped to a 2-1 loss at Morecambe.
Cambridge United's poor run of form continued with a 2-2 draw at Exeter City, Accrington Stanley beat Oxford United 1-0 and Newport County drew 1-1 with Tranmere Rovers.
Elsewhere, there were goalless draws in the games between Stevenage and Bury as well as Dagenham and Redbridge versus Portsmouth.
