Alex went into the match second from bottom in the table with their only win on the road being the 4-1 victory at Hartlepool on December 28.
But they halted Southend's two-match winning home run with an assured performance.
The Railwaymen took the lead in the 35th minute after veteran striker Dougie Freedman brought down Clayton Donaldson.
Left wing-back Billy Jones curled a fine 25-yard free-kick into the top right-hand corner of the goal with Shrimpers goalkeeper Steve Mildenhall caught flat-footed.
Donaldson nearly doubled the visitors' advantage two minutes from half-time when his shot from the left flashed across the face of the goal before going inches wide.
An earlier 30-yard effort from the frontman went straight at Mildenhall, while Byron Moore headed just wide.
Southend had been frustrated as Crewe put five men across the back when they attacked, meaning most of their efforts were from distance.
Franck Moussa fired straight at goalkeeper John Ruddy and Freedman shot just over the bar from the edge of the box.
But the Blues' best chance of the half came when Freedman fed strike partner Theo Robinson, who chested the ball down and volleyed, forcing a diving save out of Ruddy.
Southend attempted to step things up after the interval but too often found themselves unable to break down the massed ranks of red shirts, with the only early chance on goal coming from a Jean-Francois Christophe effort from 25 yards which went wide.
Crewe were happy to soak up the pressure and attack on the break, and they should have doubled their advantage after 70 minutes when a Jones free-kick was headed to Tom Pope but he missed a sitter, shooting wide of the goal.