Lee turned and fired into the top corner in the 28th minute and Hearts survived some late pressure with the help of some fortune when Steven Whittaker’s 25-yard strike hit the inside of one post and spun across the line and beyond the opposite post.
Hearts had suffered five consecutive away defeats against Hibs and the 1-0 win was their first on the road since a triumph at Dundee on October 23 kept them top of the Ladbrokes Premiership.
This win, which came without a repeat of any of the ugly scenes which marred the previous derby at Tynecastle, saw Hearts jump into fifth place and move seven points clear of their eighth-placed Edinburgh rivals.
Hibs had 10 players missing including Martin Boyle, Mark Milligan and Jamie Maclaren, the three Australia internationals who have joined up with their country ahead of the Asian Cup.
Neil Lennon still managed to name an experienced side, with Sean Mackie, Whittaker, Daryl Horgan and Oli Shaw coming in.
The visitors had centre-back Clevid Dikamona back from injury as both teams lined up with three-man central defences.
Some sloppy clearances contributed to a slack start by Hibs but Steven Naismith’s knockdown just drifted away from Peter Haring when Hearts looked like they might get in.
Horgan started to cause trouble running at the Hearts defence, his cross just too high for Shaw to head below the bar.
Hearts sweeper Michael Smith forced a decent stop from Adam Bogdan following a well-rehearsed corner routine before the opener came out of nothing as Lee collected the ball 22 yards out with his back to goal and Paul Hanlon tight on him.
The former Luton midfielder managed to turn and quickly fire a left-footed strike into the top corner.
Hibs soon threatened when Stevie Mallan’s free-kick found Whittaker but the wing-back could not generate the power to beat the diving Colin Doyle.
Naismith was handed the chance to double the lead seconds after the restart when Darren McGregor failed to deal with Sean Clare’s header on, but Bogdan parried the striker’s volley.
Hibs were being restricted to long-range efforts - Shaw hit the top of the bar with a half-volley and Mackie twice came close - and Hearts began to get in behind as the game entered the final quarter.
Naismith twice played Clare through but Bogdan saved from the first chance and the midfielder was harshly booked for diving in the box at the second opportunity after going down under Efe Ambrose’s attention.
Whittaker’s luck was out in the 79th minute when he fired low against a post from 25 yards and Hearts survived some aerial pressure with Doyle foiling Florian Kamberi from close range before saving from Mallan deep into stoppage time.