Ladislav Krejci and Vaclav Kadlec scored within the first 10 minutes to give Sparta a flying start in the Group I fixture.
Ondrej Svejdik added the third on the stroke of half-time and, although their beleaguered Israeli opponents pulled one back through Shimon Abuhatzira in the 76th minute, it mattered little.
Sparta extended their unbeaten home run in Europe to 10 matches and remained second, five points clear of tonight's opponents and Athletic Bilbao.
Kiryat Shmona goalkeeper Daniel Amos had already been forced to make a fine save from Dan Einbinder's drilled 12-yard effort when he was beaten in the seventh minute, albeit unfortunately.
Krejci's volley from Tomas Zapotocny's cross was excellently stopped by Amos, but the Sparta midfielder followed up to tap over the line.
It was 2-0 three minutes later when Josef Husbauer put Kadlec through on the right side of the area and the striker brilliantly hammered a shot across a helpless Amos.
It was one-way traffic and Kadlec fired over from the edge of the area before Svejdik added the third just before half-time.
Marek Matejovsky's cross to the back post was headed back across goal by Jiri Jarosik to leave Svejdik with an easy header into the net.
To the visitors' credit they refused to give up and Dusan Matovic's strike was fumbled by Sparta keeper Tomas Vaclik with no one able to follow up.
Their endeavour was rewarded when Abuhatzira chipped over Vaclik after being released by Adrian Rochet 14 minutes from time.
Although the visitors valiantly pushed forward, Sparta held firm to claim an ultimately comfortable win.