The result sees Sale tumble out of the top three, thereby tumbling out of a Premiership semi-final spot, and sees Leicester stretch their lead at the top to nine points.
Goode's performance, both from hand and tee, was a timely reminder for Sir Clive Woodward, who announces the Lions team on Monday.
Sale wing Mark Cueto, who is virtually assured of a tour place scored a brace of tries of his own, but there was precious little else to offer from the Sharks, with Moody and Corry dominant in the loose.
They led for the first 25 minutes, though, thanks to Cueto shrugging off some limp tackles wide on the right and jetting past his probable Lions team-mate Geordan Murphy to the line with Hercus converting.
Mike Hercus added a penalty and Goode replied with a 15th minute drop-goal before Leicester struck with four tries in 16 minutes before the break.
Moody emerged from the bottom of the pile after one line-out drive, then the flanker created Leicester's second when he scooped up a loose long throw from Andy Titterrell and the ball was whipped away for Lloyd to cruise into the corner.
Another self-inflicted wound followed when scrum-half Bryan Redpath hesitated behind another scrappy line-out and his pass was intercepted by Goode who accelerated away on a 50-metre run to the line.
Martin Johnson secured the bonus point before the break when he barged round the side of a ruck from another line-out drive and Goode's fourth conversion gave his side an unassailable 31-10 lead at the break.
Any possibility of a second half miracle was erased immediately after the break, when Tuilagi scored a marvellous try from Goode's break, via the hands of Lloyd and Murphy.
Cueto added a second – his eighth Premiership score of the season – when he outflanked some static defenders on the right.
Tom Varndell replied on the hour, though, when a series of dynamic breaks saw Corry and Moody link up with Gibson to put the winger into the left corner. Goode converted to complete an unblemished afternoon's goal-kicking.
The momentum drained out of the game after that in a shapeless final quarter with Leicester prop Graham Rowntree and Sale lock Chris Jones both sin-binned by referee David Rose.
For Leicester:Tries: Moody, Lloyd, Goode, Johnson, Tuilagi, VarndellCons: Goode 6Drop goal: Goode
For Sale:Tries: Cueto 2Con: HercusPen: Hercus
Leicester Tigers: 15 Geordan Murphy, 14 Alesana Tuilagi, 13 Leon Lloyd, 12 Daryl Gibson, 11 Tom Varndell, 10 Andy Goode, 9 Scott Bemand, 8 Martin Corry, 7 Lewis Moody, 6 Will Johnson, 5 Louis Deacon, 4 Martin Johnson (captain), 3 Darren Morris, 2 George Chuter, 1 Graham Rowntree.Replacements: James Buckland, John Rawson, Henry Tuilagi, Neil Back, Harry Ellis, Ollie Smith, Ross Broadfoot, Sam Vesty, Austin Healey.
Sale Sharks: 15 Jason Robinson, 14 Mark Cueto, 13 Chris Rhys Jones, 12 John Payne, 11 Steve Hanley, 10 Mike Hercus, 9 Bryan Redpath, 8 Sebastien Chabal, 7 Andy Titterrell, 6 Jason White, 5 Dean Schofield, 4 Chris Jones, 3 Stuart Turner, 2 Sebastien Bruno, 1 Andrew Sheridan.Replacements: Barry Stewart, Johnny Roddam, Peter Anglesea, John Carter, Magnus Lund, Fenandez Lobbe, Jos Baxendell, Sililo Martens, Richard Wigglesworth, Ben Foden.
Referee: David RoseTouch judges: Bob Mullis, Andy WatsonAssessor: Paul Bridgman