Erik Lamela scored his first goal for Tottenham to put the Group K leaders ahead, before Jermain Defoe doubled the lead from the penalty spot to become their all-time leading scorer in European football.
Ismail Isa did reduce the arrears but Sheriff could not complete the comeback.
Anzhi Makhachkala are also on the verge of progression from Group K after midfielder Karlen Mkrtchyan’s 94th-minute goal gave them a 1-0 win at Tromso
Rubin Kazan secured their place in the next round with a 1-0 win over Wigan Athletic, Oleg Kuzmin's strike midway through the first half clinching the points for the Group D leaders.
Valencia will join them in the knock-out phase after a Pablo Piatti double and a late strike from Canales earned them a 3-2 win at St Gallen, who saw defender Philippe Montandon dismissed in the second half.
Kuban Kransnodar denied Swansea City with a late goal for the second time in as many matches, Ibrahima Balde scoring two minutes into added time to put the Welsh side’s qualification on hold after Wilfried Bony had given them the lead.
Ryder Matos and Borja Valero scored two goals in four minutes as Fiorentina came from behind to qualify with a 2-1 win at Pandurii.
The Italian side’s Group E rivals Dnipro are also through after beating Pacos Ferreira 2-0.
Salzburg and Esbjerg both progressed from Group C with victories, the Austrian outfit cruising to a 3-1 win at Standard Liege, while Danish side Esbjerg overcame Elfsborg 1-0.
Bulgarian side Ludogorets became the first side to qualify from Group B despite labouring to a 1-1 draw with Ukrainian side Chornomorets, and PSV boosted their hopes of qualification with a 2-0 win over Dinamo Zagreb.
Midfielder Eran Zahavi and attacker Barak Itzhaki both scored doubles as Maccabi Tel-Aviv beat Eintracht Frankfurt 4-2, while APOEL edged out Bordeaux 2-1 in the other Group F game, despite the dismissal of Mario Budimir.
Striker Sergio Floccari scored twice to help Lazio to a 2-1 victory against Apollon, but they sit second in Group J after Trabzonspor won 2-0 at Legia Warsaw.
Attacker Chuli scored in the fourth minute of injury time to hand Real Betis a 1-0 triumph at Vitoria Guimaraes, and they now control Group I following Lyon’s 1-1 draw with Rijeka.
Betis' city rivals Sevilla suffered a setback as they could only draw 1-1 against Czech side Slovan Liberec, and Bundesliga outfit Freiburg played out a goalless stalemate at Estoril.
Midfielder Celso Ortiz scored the only goal of the game in AZ's 1-0 win over Shakhter Karagandy, while Dieumerci Mbokani’s sending off had no impact on Dynamo Kiev as they beat Thun 2-0.
Elsewhere, Zulte-Waregem won 1-0 at Maribor, Genk were held 2-2 by Rapid Vienna, while Maccabi Haifa and PAOK settled for a goalless draw.