The visitors were in front on 17minutes as from a short corner Luka Modric squared the ball to Lennon on the edge of the box, who had time and space to pick out the top corner with a curling right-foot effort.
Phil Brown's men were then back on level terms thanks to lacklustre defending from Spurs. Andy Dawson whipped in an inswinging corner from the right which saw the ball escape the hands of Carlo Cudicini, bounce off Wilson Palacios and land at the feet of Turner, who made no mistake from close range to register his fourth league goal of the season.
Darren Bent created a chance for himself early in the second half but his turn and shot from 20 yards was comfortably saved by keeper Matt Duke.
Palacios was next to try his luck for Tottenham as Robbie Keane spotted the run of the Honduras international on the edge of the box, but the midfielder's blistering first-time effort was well blocked by ex-Spurs centre-back Anthony Gardner.
Redknapp's men then came within inches of re-taking the lead as a curling free-kick from Modric found the head of Vedran Corluka inside the box, whose powering effort from six yards sent the ball crashing on to and over the Hull crossbar.
Kamil Zayatte then struck the woodwork for Hull as a left-foot corner from Dawson was met by the head of the Tigers midfielder, but his glancing effort from eight yards smacked against the right-hand post.
Spurs regained the lead with five minutes left on the clock as Benoit Assou-Ekotto swung in a cross from the left towards the towering Woodgate, who nodded the ball with precision past keeper Duke and into the top left-hand corner from six yards.