Starting on 65-1, the positive pair of Sol Budinger and Ben Mike (41) took their stand to 88 before Fernando struck twice in mid-morning.
Fernando, the first player from Sri Lanka to represent the daffodil county, had Mike lbw and induced Budinger to sky a pull.
Hill survived a loud shout for caught behind first ball but took the initiative as Handscomb started watchfully before moving through the gears.
The Australian’s no-nonsense knock was chanceless until he top-edged Andy Gorvin to mid-wicket, while Hill shrugged off the previous toils of leadership as he struck 15 fours and a six before he called a risky single to Sam Northeast at mid-off and was run out.
Gorvin quickly sent back Rehan Ahmed as Leicestershire lost three wickets in the space of 11 runs, and Fernando returned with the new ball to get rid of the slow-starting Ben Green for 10 and Tom Scriven for 12.
But Wright, promoted to 10 in the absence of Rishi Patel with a dislocated thumb, added to Glamorgan’s distress as he dominated a stand with Ben Cox and made the home attack look toothless, with Timm van der Gugten having a rare blank day.
Wright cruised to his 15th first class half-century with an array of confident boundaries as he and Cox, coming together with the score on 324, earned Leicestershire a fourth batting point.
The ninth-wicket stand left Glamorgan with a mountain to climb to save the match over two days, even assuming the wicket continues to improve in the sunshine.
Wright struck 12 fours and two sixes to move within sight of a career-best.
BBC News
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