Wales international striker Sam Vokes came off the bench to find an equaliser after the Belgian had opened the scoring 11 minutes after the break.
Mauricio Pochettino made seven changes from the side that gained that memorable 5-3 victory over Chelsea on New Year’s Day.
Chadli, Federico Fazio, Jan Vertonghen and Christian Eriksen were the only four to retain their places in the starting line-up, with Michel Vorm, Vlad Chiriches, Ben Davies, Mousa Dembele, Benji Stambouli, Paulinho and Roberto Soldado all coming in. Meanwhile, there was a spot on the bench for 17-year-old midfielder Josh Onomah.
The first half was hardly memorable, however, with not one shot recorded from either side as both teams toiled to produce anything meaningful in possession.
Spurs, roared on by our fantastic travelling support, who made the long trip north to pack out the away end, arguably had the better of the half and regularly threatened down the right hand side, with Chadli driving at the Burnley defence and Chiriches on the overlap from right-back.
But little came of our forays forward, and the same can be said of what happened at the other end, with the now regular defensive pairing of Fazio and Vertonghen marshalling a solid back four.
Things certainly livened up after half-time, when the in-form Harry Kane replaced Stambouli, who had picked up a booking early on.
Almost straight away, the striker won a corner that was cleared to Chadli, who crossed for Fazio to head towards goal for the game’s first effort on target.
England Under-21 front pairing Kane and Danny Ings then both had decent attempts at either end before the deadlock was broken on 56 minutes by another of our star performers against Chelsea.
Chadli found time and space to bring down a Davies cross from the left and fired home past Tom Heaton, who got a hand to the shot.
We looked to build on the lead almost immediately when Kane linked up with Soldado but fired straight at Heaton at his near post.
But our momentum soon faded and the home side went on to have the better of the latter stage of the half, which ultimately resulted in their equaliser.
On 69 minutes, a looping Kieran Trippier cross was headed wide at the back post by Michael Keane, before the Clarets’ best chance of the game a minute later.
Chiriches was robbed in possession by substitute Vokes, who then played in George Boyd to square for former Spur Dean Marney to fire over from six yards.
It was a warning sign that wasn’t heeded, and when Michael Kightly broke down our left-hand side on 73 minutes, Vokes made no mistake with his low cross.
Things nearly went from bad to worse a minute later when Ings’ deflected shot from distance almost caught out Vorm, but the keeper managed to hold.
Chadli and Vokes both had further openings in the closing stages, with Kane uncharacteristically failing to convert a Davies cross from yards out in the dying seconds.
So the sides were forced to settle for a replay back at the Lane next week, with a home tie against Leicester awaiting in the Fourth Round.
Spurs (4-2-3-1): Vorm; Chiriches, Fazio, Vertonghen (c), Davies; Dembele, Stambouli (Kane, 46); Chadli, Paulinho, Eriksen; Soldado (Townsend, 67). Substitutes not used: Friedel, Dier, Naughton, Capoue, Onomah.
Burnley (4-4-2): Heaton; Trippier, Keane, Mee, Lafferty; Kightly, Arfield, Marney (c), Boyd (Wallace, 78); Barnes (Vokes, 61), Ings (Sordell, 78). Substitutes not used: Gilks, O’Neill, Reid, Jutkiewicz.
Goals: Burnley - Vokes, 73; Spurs - Chadli, 56.
Yellow cards: Spurs - Stambouli, 10.
Referee: Roger East.