Spurs head coach Juande Ramos restored skipper Robbie Keane and Dimitar Berbatov to the starting line-up, with Jermain Defoe and Darren Bent relegated to the bench.
The home side made the brighter start, with Bebars Natcho firing a left-foot shot narrowly wide of the near post from just inside the area after a smart turn.
Play then became bogged down in midfield, with Berbatov struggling to find any space to cause problems to the Hapoel defence.
However, Spurs made the breakthrough 26 minutes in as Keane played in Steed Malbranque on the left and then surged forward to meet the Frenchman's cross with a crunching right-foot volley into the corner of the net.
On the half-hour Berbatov saw his initial shot blocked, but his follow-up header from Malbranque's return cross from the left made the score 2-0 to Spurs.
Seven minutes before the break Berbatov was denied by home keeper Vincent Enyeama and Keane's follow-up was deflected wide.
Shortly after the restart, Hapoel's task was made even harder as they were reduced to ten men when Gal Shish was shown a second yellow card for a crude lunge on Aaron Lennon.
Spurs then enjoyed plenty of possession, being content to knock the ball around and wait for an opening to present itself.
Twenty-five minutes from time Keane dragged a shot wide from 12 yards out after finding space in the area.
Late on Hapoel came close to earning a consolation as Fabio Junior powered clear of a hesitant defence, only to be denied by a superb block by the onrushing Paul Robinson.
Sub Darren Bent then struck the upright after rounding keeper Enyeama, as Spurs ran out well-deserved winners.