Varndell scored twice in the opening half but four tries before the break for Leicester from Matt Smith, Ben Youngs, Billy Twelvetrees and Tom Croft put the Tigers firmly in control.
Dave Walder's boot pulled Wasps level at 30-30 with nine minutes remaining before Haughton's sensational winner.
Meanwhile Exeter fly-half Gareth Steenson kicked 17 points as the Chiefs won 22-17 against a hard-working Newcastle.
A tense first-half saw both sides swap penalties and converted tries to make it 10-10 at the break.
Steenson converted a further two place kicks shortly after the restart, before Falcons centre Rob Vickerman went over to give his side the lead.
But Steenson settled Exeter's nerves with two further penalties.