The visitors fell behind midway through the first half when Bořek Dočkal's free-kick was deflected into the net by Hapoel defender Ben Bitton.
David Lafata put clear daylight between the teams with a well-executed finish seven minutes before half-time.
Sparta enjoyed the better of the second half, although substitute Ben Sahar, the former Chelsea striker, was unlucky to be denied by the post after joining the action from the bench.
Maccabi visit Group D leaders Zenit on November 24, while Hapoel host Inter at the Turner Stadium.
GROUP D
1. Zenit Pl. 4, Pts. 12
2. Dundalk Pl. 4, Pts. 4
3. Maccabi Tel Aviv Pl. 4, Pts. 4
4. AZ Alkmaar Pl. 4, Pts. 2
GROUP K
1. Sparta Prague Pl. 4, Pts. 9
2. Southampton Pl. 4, Pts. 7
3. Hapoel Beer Sheva Pl. 4, Pts. 4
4. Inter Milan Pl. 4, Pts. 3