Twumasi, who has been touted as one of the successors to Black Stars captain Asamoah Gyan, opened the scoring from the spot by the 33rd minute after Dmitriy Shomko's free-kick was handled by Dor Peretz.
He added another goal nine minutes later, after connecting a superb pass from Shomko and sending his effort beyond the reach of goalkeeper Predrag Rajkovic.
Although, Maccabi threatened Astana's defence to reduce the deficit before the break and possibly come into the game, they were not successful.
Congo DR international Junior Kabananga added another goal just two minutes after the break, before he combined with Shomko to score his second of the day and his side's fourth.
Twumasi has now taken his season's tally to 14 goals in 28 games in all competitions, while his club has incredibly gone 16 European home games unbeaten.
Astana have temporarily moved to the summit of the table with five points, one point above Villarreal and Salvia Praha, who will lock horns later in the day.