The brace from 34-year-old Charnley in 11 second-half minutes knocked the stuffing out of the Giants, who saw a 10-point deficit doubled with 11 minutes left.
Jacob Gagai grabbed Huddersfield’s third try just before the hooter, finishing a burst from halfway down the left flank, but in truth they were never close enough on the scoreboard to trouble their hosts.
This has been a puzzling season for Leigh, who started it by beating Leeds Rhinos on the opening weekend but then won only one of their next six, a Golden Point win over Toulouse at the end of March.
That narrow win seems to have ignited belief within the dressing room with the Leopards having won three of their last four to make some upward progress.
Victory never looked in much doubt from the moment Towse went over on the left flank.
Huddersfield might point to a host of marginal calls which went against them, including a possible knock-on in the build up to that first try.
But while Adam Swift levelled matters with his first try of the Super League campaign, Leigh responded immediately as Senior and Lam extended the lead to 16-4.
Giants had a try from Asher O’Donnell ruled out for obstruction but Taane Milne did barrel over to make it 20-10 at the break.
The second half proved to be all about Charnley, exactly 16 years to the day in 2010 when he made a first senior appearance for Blackpool Panthers on loan from Wigan.
His first try was a brilliant one-handed finish tight against the right touchline which showcased all his skill, while his second proved he remains a formidable force on the hoof with a muscular charge driving through Niall Evalds’ defences.
The veteran winger came within inches of marking his milestone with a hat-trick, only to narrowly fail to gather a pass with the line beckoning.
But his two tries still moved him closer to Leeds Rhinos veteran Hall, who has four in seven appearances this season.