Gloucestershire 110 (Roderick 51, Stevens 3-19) and 61 for 1 require a further 47 to beat Kent 64 (Taylor 4-20, Miles 3-11) and 153 (Bell-Drummond 61, Higgins 5-22)
Gloucestershire's bid to complete a Specsavers County Championship win inside five sessions over Kent was scuppered when rain stopped play in Canterbury with the visitors 47 runs short of their victory target with nine wickets in hand.
Chasing a modest target of 108 for victory over their Division 2 rivals, Gloucestershire had reached 61 for 1 after 15.5 overs when showers and bad light forced the teams from the Spitfire Ground, St Lawrence to ruin west country hopes of wrapping up victory in this rain-delayed game with a day to spare.
On a Canterbury pitch enlivened by heavy midweek rain that waterlogged the outfield and led to the loss of the game's first four sessions, it was Gloucestershire's seam bowlers who fared best in twice skittling the hosts for an aggregate match total of 174.
Gareth Roderick's gritty 51 helped Gloucestershire secure a valuable first-innings lead of 46, after which Ryan Higgins held a swing-bowling masterclass, taking 5 for 22 to dismiss Kent for 110 second time around.
It was a great Championship debut for Higgins with Gloucestershire - a county he chose to join from Middlesex in search of precisely this sort of opportunity
Contrasting knocks from Daniel Bell-Drummond, who hit 61 from 63 balls with 10 fours and six, and a patient 32 in a shade over two hours by Zak Crawley, marginally saved Kentish face, but the domination of Gloucestershire's bowlers continued thereafter as Dan Worrall and Matt Taylor claimed two wickets apiece in a controlled and skilled display of seam and swing-bowling in helpful conditions.
Bell Drummond's demise - his was the 11th of 15 lbw decisions in the match to date - sparked Kent's second collapse in as many days as five wickets fell for 24 runs in 10 overs either side of lunch. Kent's acting captain Joe Denly bagged a pair, Darren Stevens departed without scoring soon after then, with a single to his name, Will Gidman nicked to the keeper to complete a miserable performance against his former county as Kent succumbed in 48.3 overs.
The visitors started the fourth and final innings of the match 30 minutes before Sunday's tea interval and soon lost Chris Dent to a Matt Henry inswinger that rearranged the left-hander's stumps.
It proved a false dawn for Kent fans however, as Benny Howell (34*) and the visitors' first-innings top-scorer, Gareth Roderick (11*), dug in after the interval to post an unbroken half-century stand that only the inclement weather could halt.
As if to rub salt in Kent wounds, they also lost seamer Grant Stewart two deliveries into his third over of the afternoon with a recurrence of a hamstring problem that ruled him out of last week's final pre-season friendly against Surrey.
At the start of day three, Kent needed only six deliveries to mop up the final two wickets of Gloucestershire's first innings.
Henry, the Black Cap paceman snared Worrall leg before with a skidding first delivery of the day, then last man Taylor was well held low at first slip as Henry marked his county debut with 4 for 33.
Stevens celebrated his 200th first-class appearance for the club with three for 19, while Stewart, Gidman and debutant Harry Podmore bagged a wicket apiece.
Weather permitting, Gloucestershire appear destined to complete a deserved victory on day four, leaving Kent with plenty to ponder after their dismal showing in this opening fixture of the domestic season.