But the statistics show that Spurs should expect anything but an easy ride when they walk out at the Rajko Mitic Stadium.
Red Star also hit the woodwork twice in quick succession just before the break as Rajiv van la Parra's shot came back off the post and Davinson Sanchez looped a header dangerously onto his own crossbar.
Kane and the Spurs squad are preparing for a hostile atmosphere at the Rajko Mitic Stadium, as Liverpool discovered in a 2-0 defeat on the same day a year ago.
The Ghana worldwide missed the first leg of the UEFA Champions League Group B match against Spurs at the Tottenham Stadium due to an injury but has recovered in time for the big game at the Marakana.
Spurs were subjected to abuse on their last trip to the Serbian capital while Red Star fans were banned from the reverse fixture a fortnight ago after racist abuse in a qualifying round.
Tourists stabbed in Jordanian city of Jerash
Police have arrested a Jordan-born Palestinian man from a refugee camp in Jerash, identified as 22-year-old Mustafa Abu Touameh. He did not specify the nationality of the attacker or of those wounded, nor give details on the severity of their injuries.
However, the feeling around north London is that it is only a matter of time before the natural order is restored; Tottenham's team is too good to be this bad. The Argentine played under 20 minutes of the game against Everton over the weekend. "He is in a very good way, he feels sorry like everyone, but he is in good form".
The win gives Tottenham a strong hold on second place in Group B, with a four-point cushion to Red Star in third.
Alessandro Del Piero now holds the record, needing just 26 games to tally 20 Champions League strikes while Ruud Van Nistelrooy (27), Filippo Inzaghi (28), Mario Gomez (32) and Rivaldo (33) round out the remaining top five.
Home and away wins over Red Star are Tottenham's only wins from its last seven games in all competitions. "We will do our best to make the three points ours", he added.
Harry Kane missed the defeat to Everton due to a virus but the club captain, who has scored 10 goals in all competitions this season, is set to return to the starting line-up in Belgrade.