Despite an impressive start to life back in the County Championship for Glamorgan, they came into the game off the back of a three-run defeat on the final ball away at Northampton in their T20 opener.
Gloucestershire named an unchanged 11 after they defeated Warwickshire by 47 runs after bowling them out for just 74 in Bristol on Friday.
Injuries for the home side saw Alex Horton and Hurle replace Dan Douthwaite and Colin Ingram.
Glamorgan got off to a sluggish start in the Cardiff sunshine, the prolific South African Jensen smashing the stumps to dismiss Will Smale in the first over.
Glamorgan captain Kiaran Carlson was also dismissed for a disappointing 18 after he struck a Marchant de Lange delivery high to mid-on.
Some sharp bowling from Gloucestershire, with spinner Jack Taylor taking 2-24, left the visitors with 45-5, but Hurle gave the home side hope after smashing four sixes on the way to his 46 run total.
With Gloucestershire requiring 158 runs to win, Afghanistan international Fazalhaq Farooqi continued a remarkable start to his Glamorgan career as he took two wickets in the first over of the second innings.
Miles Hammond steadied the ship for the visitors, hitting 10 boundaries en route to 56, before being bowled by Ned Leonard.
James Bracey fell to a rare hit-wicket dismissal, kicking the stumps as he tried to boot away a ball from Leonard.
Jack Taylor looked to have swung momentum Gloucestershire’s way with 34, until he was caught on the boundary off Mason Crane, who finished with 2-16.
The partnership of Dhariwal and Matt Taylor looked up against it, but Dhariwal hit a six on the first ball of the final over from Farooqi and Taylor’s edge completed the job for the visitors.
Gloucestershire captain Jack Taylor said: “We’re elated to get over the line, it looked like it was getting away from us there but we’re buzzing to be two from two after batting really poorly two nights in a row.
“The club did an awesome job in identifying [Jansen], to get him in when Liam Scott and David Payne were out for the first half of the tournament. All the bowlers have bowled brilliantly, they’re the reason we’ve won two games.
“You always take anything around [158 to chase] here with the small boundaries. Being 7 for 3 off 10 balls is never ideal but Hammo had a great knock and losing a couple wickets we were still in a position to win at the end.”
Glamorgan’s Henry Hurle said: “It was a shame not to get over the line in the end and that’s two games we’ve lost by small margins, but I think there’s good things that have come out of the first two games.
“You’re never out of the game in T20 and they did well to get the win, but it was a massive shame for us.
“I used to come and watch them as a kid so to go out there and join the boys was really special. I’m very happy, it’s just a shame we couldn’t put the icing on the cake.”