Leicester dominated the line-out, stealing getting on for half of Northampton's throws on a difficult day for Saints' England hooker Dylan Hartley.
Northampton made a dream start when, with just 55 seconds gone, full-back Foden sold a dummy to race away for a sparkling try, Myler adding an excellent touchline kick.
But Flood reduced the arrears with a penalty before major involvement from Murphy and Ayerza culminated in Newby forcing his way over.
Flood missed the conversion and that helped Northampton regain the lead with a Myler penalty making it 10-8 to the visitors with only 12 minutes played.
But the outside-half missed the chance to extend that lead when he fired a long-range penalty attempt wide.
The lead then changed hands once again as Alesana Tuilagi made a storming burst into the 22, Saints were penalised and Flood kicked the goal.
After missed penalty opportunities from both sides, Leicester held a narrow 11-10 lead at the interval, which Flood added to when he landed a 35m penalty two minutes into the second half.
Myler again reduced the gap to a point with a penalty after the Tigers were penalised for infringing after an impressive Saints drive at a scrum.
Flood responded with his fourth penalty but, after brilliant work from Foden and Paul Diggin to gain a position in the Tigers 22, Myler's boot made it 17-16 going into the final quarter.
It was nip and tuck between the two old rivals but with 16 minutes left Crane battered his way through the Northampton defence to set up a ruck in the visitors' 22.
When Leicester moved the ball out, Ayerza was able to force his way over for the crucial try.
Flood converted before stretching his side clear with a fifth penalty after Mark Sorenson was sin-binned.
Leicester Tigers director of rugby Richard Cockerill:
"It was a great win for us. I thought it was a great battle between two good sides, especially in the set-piece.
"They probably had the better of the scrum but we nicked a fair amount of their line-out ball. We deserved our win.
"Geordan Murphy went over on his ankle. We are hoping for the best but it's too early to say the extent of his injury."
Northampton Saints director of rugby Jim Mallinder:
"To lose two of our England men was not the best but I am not blaming that for the result. Leicester played better than us.
"They have the biggest and strong back line and I was impressed with them.
"It's a very difficult place to come and play. The crowd get behind them and it does have an effect on referees."
Leicester: Murphy; Smith, M Tuilagi, Allen, A Tuilagi; Flood, Youngs; Ayerza, Chuter, Castrogiovanni, Deacon, Skivington, Waldrom, Newby, Crane.
Replacements: Agulla for Murphy (71), Cole for Castrogiovanni (53).
Replacements: Ansbro for Ashton (27), Geraghty for Downey (70), Dreyer for Tonga'uiha (75), Sharman for Hartley (66), Mercey for Mujati (75), Clark for Lawes (10), Sorenson for Day (62), Cummins for Geraghty (72).
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