Spurs boss Harry Redknapp stuck to his guns by selecting a below-strength side, with his focus firmly on Sunday's Carling Cup final against Manchester United.
Shakhtar, meanwhile, were hoping to finish off the tie after winning the first leg 2-0 in Ukraine.
Early on Jadson fired a shot wide for the visitors, before Willian wasted a fine opening after Jadson had reached the by-line and pulled the ball back across the face of goal.
Twenty minutes in Heurelho Gomes was forced to make a smart save, getting down low to turn away Fernandinho's long-range drive.
Just before the half-hour mark, Gilberto was in the right place to clear Fernandinho's effort off the line following a Darijo Srna corner.
Fraizer Campbell was twice denied as penalty shouts were waived away and then Gomes had to react quickly to turn away a Razvan Rat long-range effort.
Gareth Bale shot straight at Andriy Pyatov shortly before half-time and the visiting keeper then did superbly to deny Pascal Chimbonda and ensure that the first half ended goalless.
Twelve minutes into the second half the tie was back in the mix as Spurs took the lead through Giovani Dos Santos, who smashed the ball home after being played in by a combination of Bale and Campbell.
Campbell was then denied a penalty for a third time after seeming to be brought down by Mykola Ishchenko.
Shakhtar passed up a chance to settle the issue midway through the second half as Marcelo Moreno shot wide from eight yards out after being set up by the impressive Jadson.
Nine minutes from time Gomes denied Jadson with a superb save, as the visitors' midfielder continued to run the show.
Jadson was again to the fore as with four minutes to play Shakhtar made the tie safe, teeing up Fernandinho to accurately finish past the helpless Gomes to make the score on the night 1-1 and the aggregate score 3-1.