The 31-year-old reached three figures off 237 balls to lead their recovery after losing both openers cheaply.
Mark Cosgrove (54) shared a stand of 101 and passed 500 runs for the season in the process as the home side closed on 252-7, with Dexter 107 not out.
Kieran Noema-Barnett (3-42) and David Payne (2-59) were the pick of a tight Gloucestershire attack.
With Division Two leaders Essex not in action this week, the match gives both sides, currently third and fourth, a chance to enhance their promotion prospects.
Dexter hit 13 fours, but Leicestershire were rarely able to dominate against some tight bowling and only managed to secure a second batting point in the penultimate over of the day.
Leicestershire batsman Neil Dexter told BBC Radio Leicester:
"It was hard work out there, but those sort of centuries mean a lot more. Credit to the way they bowled, they didn't give us many bad balls and they fielded pretty well - a lot of my best shots were stopped in the field.
"I think every batsman applied themselves, we did lose one or two quickly which can happen, but we're still in there and we still have a chance to get to 300 plus.
"As a bowling unit we pride ourselves on patience, and that is what's needed out there - you aren't going to blast a team out, you have to bowl well to get your rewards."
Neil Dexter hit his second Championship century for Leicestershire on day one against Gloucestershire at Grace Road.