Morecambe were disappointing throughout and only once seriously tested Notts goalkeeper Russell Hoult, who proved equal to making the save from a glancing header in the second half by frontman Rene Howe.
An tepid first period was lit up seconds before the break by a quality goal that turned out to be the winner.
The move was instigated by defender Jamie Clapham down the left flank and his cross was flicked on delightfully by Delroy Facey to the feet of Sean Canham.
The big centre-forward took aim from precisely the same spot with which he had forced a cup replay with Kettering, but this time drilling the ball passed Barry Roche.
The second half provided more thrills and entertainment than the first and the best pass of the whole 90 minutes was a 40-yard diagonal ball from man-of-the-match Jay Smith.
He picked out Myles Weston, who waltzed passed three defenders only to see Facey's volley well saved by Roche.
Better was to follow 12 minutes from the end when Weston brilliantly nut-megged Henry McStay before again feeding Facey, who crashed his finishing effort against the bar.
The longer it went the more Notts threatened to score a second goal, but it was not to be and, in the end, the points were earned not only by Canham's goal but also by the first clean sheet at home since August.
Notts lost their on-loan midfielder Matt Wedderburn with a facial blow near the end but he was said afterwards not to be seriously hurt.