Spurs eventually broke the deadlock 10 minutes from time when Ahmed Elmohamady was adjudged to have handled Jan Vertonghen's cross inside the area.
Soldado stepped up and calmly sent Steve Harper the wrong way as he netted his fourth Premier League goal of the season.
The visitors defended well and limited Spurs' opportunities before Soldado coolly slotted home his third match-winning penalty of the season with the 1-0 victory moving Tottenham back into the Premier League's top four.
It was a frustrating first half for Andre Villas-Boas' side, who saw Paulinho squander the best of the early chances when he could only divert Lewis Holtby's free-kick over the bar, before Andros Townsend tested Harper with a dipping effort from range.
Hull, who were forced into making six changes, also had their fair share of chances as Hugo Lloris was forced into smart saves from Yannick Sagbo and George Boyd, while Tom Huddlestone's powerful volley just evaded the bar on his return to the Lane.
Despite not being as defensively minded as West Ham had set out when they won 3-0 at Spurs earlier in the month, Hull's containment plan worked to great effect in the first 45 minutes.
Steve Bruce sent his side out with Sagbo operating as a lone striker with five defenders named in an attempt to curb the influence of Spurs' wingers Townsend and Aaron Lennon.
Paulinho hooked a Holtby free-kick just over Harper's crossbar as the home side created the first clear-cut opportunity of the game after 12 minutes and Townsend then came close to continuing his fine goalscoring form with a dipping effort from 25 yards which Harper pushed behind for a corner.
The Tigers did well in the early stages, troubling Spurs and forcing a number of corners whilst restricting the service to the likes of Soldado at the other end.
Lloris was called into action for the first time shortly afterwards but George Boyd's long-range effort was straight at the France captain with the returning Huddlestone flashed a rising volley over the bar as Villas-Boas cut an inceasingly frustrated figure on the touchline.
Vlad Chiriches danced through a couple of challenges before being fouled by Liam Rosienior, who was booked, as the half ambled towards a conclusion and the resulting free-kick was rolled into the path of Kyle Walker whose rasping effort was pushed clear by Harper.
Spurs looked sharper at the start of the second half and Soldado came close to opening the scoring but could only scuff a shot at Harper after the Spaniard had been slipped in by Townsend.
Referee Michael Oliver did give a free-kick to Hull as they broke forward, booking Chiriches for bringing down Sagbo after the summer signing from Evian had brushed past him.
Hull continued to keep men behind the ball and frustrate Spurs as Villas-Boas introduced Christian Eriksen and Jermain Defoe from the bench as he looked to inject fresh impetus in to his side.
The deciding goal came from the penalty spot in the 79th minute as Elmohamady was adjudged to have handled a Vertonghen cross from the edge of the box.
Bruce was livid with the decision as the Egypt international was in close proximity to Vertonghen but the ball struck him on the hand and Soldado stepped up to convert his third penalty of the season.
Townsend then required lengthy treatment after he crashed into the advertising hoardings and fell into the photographers' pit behind the Hull goal and returned with a bandaged wrist.
Hull substitute Robbie Brady hit a set-piece straight at Lloris before Huddlestone arrowed an injury-time free-kick wide of the goal as Spurs held on to return to the UEFA Champions League berths.