The 27-26 defeat leaves Newcastle anchored at the foot of the table and they will count themselves hard done by in the closing stages especially in the final seconds when the referee could easily have awarded them a potential match-winning penalty.
In a match which swung one way and then the other, Ed Slater scored the opening try for Leicester, but Greg Goosen put the home side in front with their opener shortly after.
Despite inconsistency from Billy Twelvetrees, at half-time the score was tied at 11-11.
Tim Swinson crashed through shortly after thee break as Newcastle moved in front once more but Julian Salvi scored 53rd-minute try before Twelvetrees put them back in front at.
Luke Fielden made it 26-22 to Newcastle with another home try but with just three minutes remaining, Leicester inched their way up to the Newcastle line and put the squeeze on at three successive scrums before engineering a gap for Mafi to score the decisive try.
There was also late drama at Northampton where a penalty two minutes from time by Tom Homer gave London Irish a 14-13 success.
Northampton were left to feel a sense of grievance as there seemed to be an Irish knock-on as Jonathan Joseph unloaded to Homer just prior to the hosts being penalised.
Northampton led 6-3 at the interval but Homer's second penalty levelled matters at the start of the second half.
The first try went to the visitors Nick Kennedy dived over in the corner.
With 10 minutes remaining the Saints twice opted not to kick penalties in favour of a kick to the corner and a forward drive, and it paid dividends when referee Martin Fox awarded a penalty try as Irish once again offended at the scrummage area.
Myler converted to put Northampton in front but there was still time for Homer's late penalty winner.
Harlequins continued their winning start to the season with a 42-6 bonus-point victory over Gloucester at the Stoop.
In wet conditions Quins' dogged pack out-fought their opponents at the breakdown and in the setpiece, resulting in two pushover tries from the impressive young flanker Luke Wallace.
Quins were also classier behind the scrum with fly-half Nick Evans a constant threat and the slick passing in the backline leading to tries for wingers Sam Smith and Ugo Monye.
For Monye it was his third in three games after being omitted from England's World Cup squad. Replacement hooker Chris Brooker rounded off an impressive showing with a fifth try as Quins claimed a third straight win of the season.
Close-season signing Fraser McKenzie opened his scoring account as Sale handed Wasps their first defeat of the season, 29-18 at Adams Park.
The 23-year-old former Scotland Under-19 captain - signed from Edinburgh - sparked a fine recovery by the Sharks, who dominated for long spells to turn the match around after trailing 10-3 after 14 minutes.
Sale's other try came from skipper David Seymour with 19 points from the boot of fly-half Nick Macleod, relishing the role of front-line kicker following Charlie Hodgson's move to Saracens.
Macleod took his points tally for the campaign to 41 from three matches with five penalties and two conversions as Sale notched their second victory of the season.
Former Sale centre Chris Bell and fly-half Ryan Davis scored the Wasps tries, with Davis adding a conversion and two penalties.
Bath scored second-half tries through Dan Hipkiss and Nathan Catt to beat Exeter 23-19 in a full-blooded derby at the Recreation Ground.
The visitors, however, claimed a losing bonus point with a last-minute penalty try, which meant that instead of slipping to third place behind Bath in the Aviva Premiership, it was the Devon side who clung on to second behind unbeaten Harlequins.
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