Allan struck after 26 minutes, finding the bottom corner from distance to beat Craig McDowall in the Alloa goal.
At the other end, goalkeeper Mark Oxley had to be alert to push away Philip Roberts’ deflected strike.
Allan grazed the crossbar with a powerful 25-yard strike in the second half before substitute Martin Boyle forced Craig McDowall into a smart stop.
Boyle then spurned a great opportunity late on when he side-footed Jason Cummings’ lay-off wide of the target.
Alloa pushed for an equaliser late on but Hibs stood firm to open up a healthy gap between themselves and third placed Rangers.
However, the Leith team’s city rivals took the plaudits and kept their 20-point advantage at the top intact with a club-record 10-0 hammering of the 10-man Blue Brazil at Tynecastle in the capital.