Ki Sung-yueng opened the scoring in the 32nd minute with a wonderful drive and Mark Wilson's shot in the 75th minute, which deflected off Well skipper Stephen Craigan, put the Parkhead men into an unassailable lead.
Charlie Mulgrew's wonderful free-kick with two minutes remaining brought an even more positive end to Lennon's first season as permanent boss - which, to say the least, has been troubled.
On the field Lennon's side were beaten to the SPL title to Rangers and also lost in the final of the Co-operative Insurance Cup final to their Old Firm rivals.
Off the field, Lennon was sent bullets and parcel bombs, and suffered an attack by a fan at Tynecastle.
A light aircraft, presumably hired by Celtic supporters, flew over Hampden at the start of the match trailing a banner with the words 'In Lennon We Trust', and that trust was repaid as his side never really looked like slipping up against a Motherwell team who found it all too much.
Before the match there a minute's applause as tribute to the late Phil O'Donnell, who played for both clubs, and former SFA secretary Ernie Walker, who passed away recently.
Lennon and Well boss Stuart McCall ran back up the tunnel following the pre-match formalities to get out of their suits and into their tracksuits to watch a scrappy first half punctuated by a couple of strange decisions by referee Calum Murray and lit up by Ki's goal.
With just over a minute gone Parkhead striker Gary Hooper knocked Kris Commons' cross on to the bar but the flag was up for offside.
But until Ki scored half an hour later, there was little action of note aside from bookings.
The ball zipped around the rain-soaked pitch making it difficult for the players, defenders especially, and in the 10th minute Celtic stopper Daniel Majstorovic was booked by referee Murray for a foul on John Sutton.
However, five minutes later, with the game still settling down, Fir Park midfielder Keith Lasley was lucky only to see yellow for a high challenge on Celtic defender Glenn Loovens which owed nothing to the conditions.
Hoops skipper Scott Brown was shown a yellow card for a tackle on Steven Hammell, before Ki also found himself in the book on the half-hour mark for a challenge on Lasley.
However, two minutes later the South Korean made a much more positive mark on the game when he picked up a Commons pass 30 yards from goal and drilled a wonderful shot past the helpless Well keeper Darren Randolph.
Lennon turned to the Celtic fans and repeatedly punched the air in what looked as much anger as joy.
By this point Fraser Forster had barely touched the ball but, as Motherwell shook themselves out of their slumber, the Celtic keeper was glad of the help of the crossbar when Gavin Gunning's shot from 25 yards off smacked off it and away to safety.
Majstorovic was then penalised for handball but referee Murray refused to reach for the second yellow card which would have seen the Swede taking an early bath.
Motherwell had shouts for a penalty turned down in the 40th minute when Loovens appeared to nudge Sutton to the ground inside the box as he went for a cross from Humphrey.
Referee Murray left his most contentious decision of the first half until last when he when he failed to penalise a prostrate Craigan for handling the ball at the edge of the penalty area as the Hoops threatened.
Play stretched from the start of the second half and in the 56th minute, as the Lanarkshire side enjoyed a rare spell of pressure, Loovens did well to take a cross from Chris Humphrey away from the head of Sutton.
Celtic broke quickly seconds later through Georgios Samaras, only for the Greece striker to be crowded out.
Commons should have doubled Celtic's lead in the 66th minute when Brown sent him clear on goal but when the Scotland midfielder poked the ball past Randolph from 10 yards, backtracking Well defender Shaun Hutchinson cleared off the line.
Anthony Stokes replaced Samaras two minutes later and was almost immediately crunched by Craigan to earn the Motherwell defender a booking.
The destination of the cup was confirmed 15 minutes from time when Commons set up Wilson and his low drive took a cruel deflection off Craigan to send Randolph the wrong way before the ball limped over the line.
In the 88th minute, after Craigan had fouled Hooper at the edge of the box, Mulgrew's left foot powered the free-kick high past the flailing Randolph to put a glossy finish on the win and leave the Celtic fans celebrating.