Jake Livermore had given Hull a half-time lead at the KC Stadium on Sunday with his first goal of the season, but he was unable to celebrate a victory against his former club.
On-loan winger Ramirez was shown a straight red card following an off-the-ball incident with Jan Vertonghen five minutes after the break and Tottenham dominated from then on.
Harry Kane equalised with his 11th goal of the season after Eriksen's free-kick had struck the post, before the Dane grabbed a late winner, as Tottenham claimed all three points from behind against 10 men - just as they did at Aston Villa in their last Premier League away game.
Mauricio Pochettino's side had been beaten by Stoke City before the international break and the Argentine coach got the response he was looking for, while Hull only have two victories to their name in the top flight this term.
Fit-again defender Michael Dawson returned to face his former club as one of six changes to the Hull side that lost at Burnley, with Allan McGregor, Ramirez, Andrew Robertson, Hatem Ben Arfa and Nikica Jelavic also starting.
Davies then spared stand-in captain Hugo Lloris' blushes when he blocked Ramirez's effort after the France goalkeeper had flapped at a free-kick 19 minutes in.
The Tottenham shot-stopper showed his class with a fine reflex save down to his left to deny Robbie Brady, before Ben Arfa blazed a shot over the crossbar after Lloris had palmed Ramirez's left-footed strike into his path.
McGregor was called into action at the other end eight minutes before half-time, palming away Lamela's well-struck shot following a swift break, and Hull breathed a sigh of relief when Eriksen flashed a dangerous ball across the face of the goal but nobody was on the end of it.
Pochettino replaced Dier, who had been booked in the first half, with Vlad Chiriches at the break and Tottenham's chances of getting back into the game were enhanced when Ramirez was dismissed five minutes into the second half.
Hull boss Bruce was furious with the decision and he was left even more frustrated when Tottenham equalised after 61 minutes. Kane was on hand to turn the ball into an empty net after Eriksen's sublime free-kick had struck the woodwork.
