The match was named in honour of Ed Slater, who played for both clubs but was forced to retire in pre-season after being diagnosed with motor neurone disease.
Former lock Slater, 34, was present at Welford Road to present the trophy.
Wigglesworth ended his playing career aged 39 after being thrust into the role of interim Leicester head coach when Steve Borthwick, together with assistant Kevin Sinfield, left the club to take charge of England.
England's Anthony Watson scored two tries for Leicester, with Guy Porter also crossing, as Freddie Burns kicked three penalties and two conversions.
Albert Tuisue and England flyer Jonny May scored tries for Gloucester, with Scotland international Adam Hastings adding a penalty in a match that sparked into life following a drab first half that ended with Gloucester 8-6 ahead.
Defeat for the visitors was made worse by the sight of Wales wing Louis Rees-Zammit going off early on with a leg injury -- a worry for Warren Gatland ahead of the New Zealander's second stint as Wales boss, which begins with a Six Nations clash at home to Ireland on February 4th.
Leicester's win saw them leapfrog the Cherry and Whites into fourth place in the table.
In Saturday's other English top-flight encounter, Exeter withstood a Bath fightback to win 20-15 at Sandy Park.
Exeter's Dave Ewers and Henry Slade both scored tries as the hosts surged into a 20-10 half-time lead.
Bath, however, dominated the second half but only had replacement hooker Niall Annett's 62nd-minute try to show for their efforts as Exeter held on for a win that kept them in play-off contention.
