The former Valencia striker broke his five-game scoring drought in style at White Hart Lane as Andre Villas-Boas' men comfortably extended their 100 percent European record
The Spaniard opened the scoring on seven minutes when he glanced Gylfi Sigurdsson's free-kick past Evgeni Pomazan, and doubled the advantage eight minutes later after good work from Erik Lamela.
Ewerton pulled one back for Anzhi just before the break but Tottenham shone again in the second half, with Lewis Holtby scoring brilliantly before Soldado claimed the match ball with a calm penalty.
It was some way for the Spaniard to mark his return to the Spurs side, while Anzhi opted to name just five of a permitted seven substitutes, possibly as a result of the cost-cutting measures that have seen the likes of Samuel Eto'o and Willian depart.
And, within 16 minutes, Soldado had fully justified his recall with a quickfire double.
The Spain international striker first applied a glancing header to Gylfi Sigurdsson's seventh-minute free-kick from a narrow angle that was awarded after Abdul Razak had upended Andros Townsend on the edge of the penalty area.
Tottenham doubled the lead shortly afterwards thanks to excellent link-up play between Lamela and Soldado, before the striker timed his run to perfection to drag a shot across Evgeni Pomazan.
Townsend spurned a decent opportunity to add a third five minutes before halftime. Sigurdsson's raking pass gave the England international a clear sight of goal, but he was left to rue a heavy touch as he snatched at his chipped shot that drifted wide.
It initially proved a costly miss as Anzhi went down the other end and pulled one back.
Brad Friedel turned Jucilei's header over the crossbar and Ewerton stuck out a boot to prod home from close range after the resulting corner bounced along the six-yard box.
A moment of magic from Holtby, though, restored Tottenham's two-goal lead 10 minutes into the second half.
Townsend worked his way inside from the Tottenham right and dinked a delicate chip over two defenders to allow Holtby to tee the ball up with the inside of his left foot before volleying it with the outside of the same boot past the goalkeeper.
Soldado was then handed the perfect opportunity to walk away with the match ball from the penalty spot after substitute Ryan Fredericks was adjudged to have been clipped by Jucilei.
In truth, it was a harsh decision, but that mattered little as Soldado duly dispatched the spot-kick and Tottenham moved on into the round of 32 as the team to beat.
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