For a long while it appeared it was going to be a struggle on a difficult pitch after AEL snatched the lead against the run of play on 14 minutes. It wasn't until the latter stages and the introduction of Erik Lamela that the tie turned, with the Argentine providing two excellent assists.
There were post-World Cup returns to the starting line-up for Jan Vertonghen and Paulinho, as well as a competitive debut for Ben Davies at left-back. Soldado was given his first start of the season up top, with Kane, Paulinho and Andros Townsend in behind him and the deeper roles were occupied by Nabil Bentaleb and Lewis Holtby.
The first chance came on four minutes when Davies cut back for Kane, whose effort came back off of keeper Fegrouch and flew into Soldado who could not direct the ball into the net.
Paulinho then shot wide after being cleverly teed up by Holtby before Kane fizzed a free-kick over from all of 40 yards on 12 minutes.
Two minutes later AEL snatched the lead with their first effort on goal. Adrián Sardinero sped through, kept his composure and slotted past captain Hugo Lloris to spark joyous scenes amongst the home crowd.
Chances came and went to level but extra passes were chosen over shooting opportunities and Fegrouch remained untroubled. Kane was unlucky not to get on the end of a Townsend cross on 26 minutes, hanging in the air but just unable to make a connection with the teasing centre.
Kane then tried his luck from 35 yards, with Fegrouch doing well to gather and hold, saving again from Kane moments later.
Lloris was required to dart from his line on 33 minutes to deny Sardinero a second on the break.
AEL had a big chance in the opening moments of the second half when Luciano Bebe attempted to force his way through before being denied by a last-ditch challenge. Carlitos then shot into the side netting after a positive run.
The first change was made in the 58th minute with the introduction of Nacer Chadli in place of Paulinho. Mousa Dembele followed eight minutes later, taking over from Holtby.
AEL were stronger in the second half, not surrendering possession so easily and clearly determined to build on their first half lead. Perhaps their positivity proved costly in the end against the likes of Lamela.
The lead nearly evaporated on 70 minutes when Kane struck the underside of the bar, just before Lamela replaced Townsend in the final change of the night from Mauricio Pochettino.
The equaliser came in the 74th minute in spectacular style. Kane surged forward before dispaching to Lamela, who launched a perfectly timed and measured chip into the path of Soldado. The Spaniard smashed home on the volley with a superbly executed strike.
Five minutes later the lead was seized when the dynamic Lamela delivered a clever through ball into the run of Kane, who then shot high into the net to turn a long-standing deficit into an advantage.
Lamela almost capped his fine cameo with a third, but turned Chadli's cross inches wide.
The scoreline remained 2-1 and we take that lead into the second leg at the Lane next Thursday, August 28.
AEL Limassol: Fegrouch, Sielis, Carlitos, Cadu, Diego Barcelos, Edmar, Luciano Bebe (Eleftheriou, 67), Guidileye, Sardinero (Carlitos, 80), Gikiewicz (Tagbajumi, 73), Nikolaou (c). Subs (not used): Pulpo (GK), Espana, Nadeau, Stavrou.
Spurs: Lloris (c); Naughton, Dier, Vertonghen, Davies; Bentaleb, Paulinho (Chadli, 59); Townsend (Lamela, 72), Holtby (Dembele, 67), Kane; Soldado. Subs (not used): Friedel, Dawson, Rose, Sandro.
Goals: AEL - Sardinero (27). Spurs - Soldado (74), Kane (79).
Yellow cards: AEL - Cadu. Spurs - Holtby, Soldado, Davies.