Lucas Moura's 85th-minute goal cancelled out a first-half Ousmane Dembele effort, and the point proved to be enough for Tottenham to advance to the next round due to the fact that Inter Milan were held at home by PSV Eindhoven in the group's other match.
Luis Suarez was left out altogether for Barcelona, while Lionel Messi, Gerard Pique, Sergio Busquets and Jordi Alba were all named on the bench as the likes of Carles Alena, Jasper Cillessen, Juan Miranda and Munir El Haddadi were handed spots in the XI.
Tottenham started well, but the English outfit found themselves behind in the seventh minute of action. Kyle-Walker Peters was making his full Champions League debut, and the right-back will not have fond memories of what occurred in the early stages.
Indeed, the Englishman was hunted down by Dembele following a cleared Tottenham corner, and the Frenchman drove away from the young full-back before finding the back of the net with an excellent finish, having put Harry Winks on the ground inside the penalty box.
Philippe Coutinho missed the crossbar with a strike in the 14th minute as Barcelona threatened once again, before Alena struck a similar effort over the Tottenham goal in the 27th minute.
Tottenham did not have their first serious chance of the match until the 30th minute. The move originated down the left, with Danny Rose finding space before delivering an excellent low cross towards Son Heung-min, but the attacker just failed to make contact.
Son had an even better opportunity in the 33rd minute after driving into the Barcelona box, but the 26-year-old saw his effort kept out by Cillessen.
Son and Cillessen again went head to head in the 38th minute, and it was the Barcelona goalkeeper that came out on top for a second time as he made the save.
Barcelona had a golden chance to double their lead in the final stages of the first period when Coutinho weaved into the Tottenham box before looking to pick out the bottom corner, but the post came to the away side's rescue.
Tottenham were the better team in the early stages of the second period, and would have levelled through Christian Eriksen in the 47th minute had Cillessen not made an excellent save.
Eriksen and Dele Alli both had shots blocked in the period that followed, and Messi was sent to warm up moments before Kane fired over the Barcelona crossbar in the 51st minute.
Walker-Peters did well to block a strike from Coutinho in the 54th minute as Barcelona had a chance to double their advantage, but Tottenham were the team on the front foot.
Erik Lamela was the first player off the Tottenham bench in the 61st minute, while Messi was introduced two minutes later for the ineffective Munir.
Eriksen had a wonderful chance to level the scores in the 70th minute when he met a deep cross from Rose, but Cillessen made another excellent save.
Cillessen made an even better stop to keep out a close-range Lucas header 15 minutes from time, and it was at that point that Inter had levelled the scores against PSV.
Tottenham were throwing six players forward each time that they had the chance to break as the Premier League club, who also introduced Fernando Llorente, desperately looked to level the scores.
Finally the breakthrough arrived in the 85th minute when Lucas turned a low Kane cross into the back of the net to hand Tottenham the goal that they richly deserved.
Rose had a golden chance to send the away side ahead in the spell that followed, but the left-back fired over the crossbar from inside the Barcelona box.
It mattered little though, with Inter's failure to overcome PSV on home soil meaning that Tottenham squeezed into the knockout round of the competition on eight points as Group B's runners-up.
BARCELONA (4-3-3): Cillessen; Semedo, Lenglet, Vermaelen, Miranda; Alena, Rakitic (Busquets 46'), Arthur; Coutinho, Munir (Messi 63'), Dembele (D Suarez 76')
TOTTENHAM HOTSPUR (4-2-3-1): Lloris; Walker-Peters (Lamela 61'), Alderweireld, Vertonghen, Rose; Winks (Llorente 83'), Sissoko; Eriksen, Alli, Son (Lucas 71'); Kane