Pete Ades shone with a maiden Home Counties half-century as the home side posted 224 all out off 48.3 overs after electing to bat.
An impressive all-round display in the field then saw Thame bowled out for 145 with Jehan Mohammed returning league-best figures of 4-29.
It was a first win for the side under new skipper Patrick Foster, who played a pivotal role with a swashbuckling 46 before picking up three wickets.
Ades had laid the foundations in his two previous innings this season without getting a score of real substance, but he put that right this time with 56 from 93 balls at the top of the order.
He shared a stand of 66 for the second wicket with new signing Shiryar Ahmed, from Reading Tigers, who made 19 before being trapped lbw by Thame skipper Hassam Mushtaq.
That sparked a middle-order collapse with six wickets going down for 65 runs as Horspath slumped to 138-7 with Kelvin Burrows (4-42) doing the damage.
His haul included Ades, but not before he went to his half-century in style with a glorious pull shot for four in the 26th over. His fine knock included eight boundaries and one six.
Foster and Will Hawtin thren put on a crucial 70 for the eight wicket to turn the innings round. The Horspath captain led the way by blasting six fours and two sixes in his 35-ball knock before the innings was wrapped up by Jonathon Jelfs (2-40), while Dinushka Malan took 2-23 from his 10 overs.
Foster's flurry of runs had given Horspath a fighting chance, and he made the breakthrough in Thame's innings when Farid Butt was caught by Amin Rafiq with 19 on the board.
Will Eason then got in on the act by trapping Luke Hayes lbw before bowling opener Michael Beard for 21 to make it 52-3.
Horspath sensed an opportunity, and Jehan Mohammed joined the attack to have Kashif Nizami caught behind by Hawtin, before Foster struck twice more to leave Thame toiling at 88-6.
Mohammed tightened Horspath's grip by winning lbw appeals against Malan and Mushtaq to make it 93-8, and there was no way back for the visitors.
Mohammed claimed a fourth victim when Burrows edged into Hawtin's gloves, before Faisal Ali and Jelfs put on a breezy 37 for the last wicket.
It was left to Lloyd Belcher to secure victory - which takes Horspath off the foot of the table - by bowling Ali for 24 in the 39th over. Mohammed's superb spell was well backed up Foster (3-36) and Eason (2-36).
Posted by: Russ