The Reds almost went in front in the eighth minute when Davide Petrucci released Federico Macheda, who rounded Andreas Arestidou but saw Laurence Wilson slide in to clear his shot off the line.
However, the Shrimps responded by enjoying the better of the next phase of play. The lively Izak Reid should have done better when racing clean through but skied his shot, Dan Parkinson forced a save out of Anders Lindegaard at his near post and Alec Naylor's glancing header dropped just off target.
Petrucci tried to gee up the visitors by testing Arestidou's alertness with a couple of attempts while the keeper made a top-drawer save to turn away Michael Keane's acrobatic overhead kick.
Bebe had already sent a couple of shots wide when he made the breakthrough after switching from the left to right flank. Tricking his way into the box past full-back Wilson, the Portugal Under-21 international clubbed a right-footed shot across Arestidou and into the corner of the net.
Arestidou was able to address Bebe's next attempt, from a Ryan Tunnicliffe lay-off, after it deflected towards him and Macheda failed to finish a fine run in the manner it deserved by dragging wide to ensure the gap remained one goal at the break.
The fact that Morecambe still remained within touching distance was largely down to the excellence of Arestidou. The former Preston keeper squeezed out Marnick Vermijl at his near post after a purposeful thrust forward by the Belgian, palmed away a Tunnicliffe shot from the edge of the