Spurs fielded an under-strength side in Ukraine, with midfielder Tom Huddlestone starting at centre-half and 17-year-old Dean Parrett handed a senior debut in midfield.
Four minutes in the home side threatened as Ilsinho's pass deflected through to fellow Brazilian Jadson, who shot wide of the far post from the right side of the area.
Shakhtar then continued to call the shots against an inexperienced Spurs line-up who seemed to lack any punch in attack.
They wasted another good chance 26 minutes in as Dmytro Chygrynskyy swung in a superb ball from the left over the head of Pascal Chimbonda, but Olexandr Gladkiy snatched at his shot and it flew well wide.
Just past the half-hour mark Giovani dos Santos caused home keeper Andriy Pyatov a problem as his shot from an acute angle hit the sidenetting.
The rest of the first half saw few openings at either end, with the game having failed to catch fire.
Soon after the restart Shakhtar went close again, as Willian found space on the left side of the Spurs area, but screwed his shot across goal and it was cleared for a corner.
However, after that escape Spurs started to enjoy plenty of possession and were content to keep their hosts at bay.
Midway through the second half Darren Bent entered the fray, with the England striker replacing Mexican Giovani.
The visitors' resistance was finally broken with 12 minutes left to play as substitute Yevgeny Seleznov netted with his first touch, heading home a Jadson free-kick as he reached the ball just before Heurelho Gomes.
Shakhtar then rubbed salt into the wounds two minutes from time as Jadson was allowed to cut in from the right, exchange passes with Willian and slot a low, left-foot shot beyond Gomes to make the final score 2-0.