Summerfield struck in the 43rd minute with his first league goal for the club since his summer switch from Cheltenham. The midfielder timed his run into the box to perfection to power home a fine header from Marvin Morgan's left-wing cross.
It was fitting that Morgan should be the provider as he provided much of the inspiration for lowly Shrewsbury in the first half and twice forced two routine saves from goalkeeper Alan Martin.
Shrewsbury's goal came just after Crewe's strong penalty claims were rejected. Lauri Dalla Valle went down in the box but referee Chris Sarginson waved play on, much to the dismay of visiting manager Steve Davis.
Morgan might have doubled Shrewsbury's lead at the start of the second half when, set free by Luke Rodgers, he was again denied by a fine save from Martin.
Crewe then rallied but Chris Weale saved well from Dalla Valle before substitute Max Clayton hooked a volley just off target as the Railwaymen's three-match winning run bit the dust.