Leicestershire 252 and 78 for 2 (Azad 38*, Higgins 2-15) trail Gloucestershire 504 for 9 dec (Dent 125, Taylor 99, Smith 84, Howell 76) by 174 runs
Having come together the previous evening, the pair kept their stand intact throughout the morning session and eventually added 157 for the seventh wicket to help their side to a first-innings total of 504 for 9 declared, a lead of 252.
Taylor fell one short of what would have been an eighth first class century, while Howell also made his highest score of the season in contributing 76. Will Davis and Chris Wright finished with three wickets each.
By the close, Leicestershire had responded with 78 for 2 in their second innings and trailed by 174. Hassan Azad was unbeaten on 38.
The day began with Gloucestershire 275 for 6 and leading by only 23. Taylor, unbeaten on 15 at the start, and Howell, who had not opened his account, had to play watchfully on a pitch offering some variable bounce for the seamers.
Leicestershire's bowlers did not enjoy much luck, beating the bat on several occasions before the two batsmen grew in confidence, Taylor, in particular, punishing anything over-pitched with some sweetly-timed drives.
He brought up a third batting point with a four and a single off Mohammad Abbas before taking a liking to the slow left-arm spin of Callum Parkinson, hitting 11 runs off his first four deliveries.
Taylor reached a 93-ball half-century, well supported by the steady Howell. At lunch the total was 387 for 6 and Gloucestershire's lead had extended to 135.
The afternoon session saw Howell go to his half-century from 115 deliveries before Taylor fell agonisingly short of a deserved ton, bowled by Davis with a ball that looked to keep a bit low. He had faced 173 deliveries and hit 12 fours.
At 430 for 7, Gloucestershire had already taken a stranglehold on the match. A further 33 had been added when Howell also fell to Davis, lbw playing down the wrong line.
A breezy 33 not out from Chadd Sayers added to Leicestershire's woes before home skipper Chris Dent closed the innings, at which point tea was taken. Davis had been the pick of the bowlers, sending down 29 overs and returning 3 for 73.
Azad and Paul Horton began the visitors' second innings in solid fashion, taking the score to 48 and seeing off the new ball attack of Sayers and loan signing Ethan Bamber before Horton fell lbw to Ryan Higgins for 26.
Horton had been dropped on 22 by Miles Hammond at second slip off Matt Taylor. Under increasingly overcast skies, with rain in the air, batting looked tricky and Hammond soon atoned by holding a sharp chance offered off Higgins by the driving Neil Dexter, who departed without scoring.
Higgins finished an impressive eight-over spell from the College Lawn End with figures of 2 for 15 before a couple of showers ended play a couple of overs early.