A first Tottenham goal for Erik Lamela and a record-breaking penalty from Jermain Defoe secured safe passage for Andre Villas-Boas' side.
Lamela has been used sparingly by Villas-Boas since his arrival from Roma and has yet to start a Barclays Premier League game for Spurs but he made the difference against the reigning Moldovan champions.
Lamela put in one of his most assured performances in a Tottenham shirt and topped it off by tucking away the first goal of the game 15 minutes into the second half, before being tripped inside the box moments later to give Defoe a chance to make history from 12 yards.
The England striker converted the penalty to claim his 23rd European goal for the club, one more than Martin Chivers managed during his time at White Hart Lane.
But Spurs did not have everything their own way. For all of their defensive work, Sheriff threatened twice in the first half before Ismail Isa grabbed a goal on 72 minutes to keep Tottenham on their toes.
Tottenham started the game brightly enough but Sheriff came with a blueprint copied from several other visiting teams in recent White Hart Lane fixtures and set out to frustrate their hosts.
Moussa Dembele had the first effort of the night after seven minutes as he rode a number of half-hearted challenges before firing in a low shot which Vjekoslav Tomic pushed behind for a corner.
Villas-Boas made eight changes from the goalless draw at Everton on Sunday and it was the returning Etienne Capoue who was next to try his luck but his similar attempt was off target.
Lamela, another player recalled for the game, had calls for a first penalty turned down after 20 minutes. The Argentina international was caught by Djibril Paye and, after originally looking to stay on his feet, tumbled over with referee Kenn Hansen unmoved.
For all of Tottenham's possession they were almost caught out in the 25th minute as Sheriff broke forward and Isa's shot deflected on to a post off the boot of Younes Kaboul.
Christian Eriksen's lapse in concentration almost gifted the visitors the lead shortly afterwards as he rolled the ball across his own penalty area and in to the path of Ricardinho, who arrowed a shot wide of Brad Friedel's right-hand post.
Spurs soon regained the upper hand as Lamela had two efforts blocked by brave Sheriff defending but it was turning in to a similar story for the home side as they failed to create any clear-cut chances.
The second half started where the first 45 minutes had left off as Sheriff looked to keep things tight at the back and limit the number of chances Tottenham's front players could create.
Friedel, who set the record for the oldest player to appear in this competition when he was named in the starting line-up, was forced in to making his first save of the evening as Luvannor Henrique curled a low effort which the 42-year-old dealt with comfortably.
Tomic in the Sheriff goal was forced in to a much smarter save just seconds later as Eriksen let fly from 25 yards, with the Croatian goalkeeper tipping his shot over at full stretch.
But Spurs finally broke the Moldovan's resilience on the hour as Lamela struck a composed shot past Tomic after Eriksen's return ball had deflected in to his path.
Lamela was again heavily involved in Defoe's record-breaking goal as he was brought down inside the box with the 31-year-old thumping home the resulting penalty to move clear as Tottenham's leading goalscorer in European competition.
Sheriff were soon handed a lifeline as Friedel could only parry a shot from Cadu with Isa on hand to finish coolly and make it an uncomfortable final 20 minutes for the hosts as they conceded their first goal of this year's competition.