Harry Kane and Christian Eriksen were able to rest up on the bench and enjoy a stunning Son Heung-min opener on the stroke of half-time.
Dele Alli headed in his 50th goal for Spurs in all competitions to make the points safe, moving Mauricio Pochettino's side back up to third in the table after Chelsea's 2-0 win over champions Manchester City earlier in the day.
Tottenham now face the daunting task of needing to better Inter Milan's result against PSV Eindhoven when they take on Barca, who were in rampant form in a 4-0 derby demolition of Espanyol in La Liga.
As Kane watched on, Spurs dominated possession with some slick play but lacked a cutting edge during the opening 45 minutes.
Son's wild and wayward free-kick summed was entirely out of keeping with what he produced in first-half stoppage-time.
Shortly after Wes Morgan produced a brilliant last-ditch tackle to deny Alli, the Korea Republic international shifted the ball on to his left foot and, from 25 yards, crashed an unstoppable strike past Kasper Schmeichel.
In an attempt to rouse his side from their creative slumber, Claude Puel brought on Rachid Ghezzal and Marc Albrighton for Vicente Iborra and Kelechi Iheanacho.
But Leicester were dealt a body blow as Nampalys Mendy coughed up possession and Son turned provider, scampering into space on the left flank to cross for Alli to power past Schmeichel's best efforts.
Eriksen and Kane were then handed late run outs before right-back Serge Aurier worryingly hobbled off and Leicester's challenge fizzled out – the ninth-placed club seeing their unbeaten Premier League run halted after six matches.
