Guy Noves' star-studded side avenged last Sunday's shock reversal at home against the same opponents, with Medard, Christopher Tolofua, man of the match Louis Picamoles and replacement Gael Fickou all crossing the whitewash in Galway.
Tolofua crashed over late in the first half to leave Connacht 22-9 behind at half-time, the province's only points coming from the boot of out-half Dan Parks, who kicked a penalty and two drop goals.
A neat lineout move put Picamoles through for his try early in the second half, and with Connacht unable to respond Lionel Beauxis added another penalty and converted Fickou's closing effort for a 12-point personal haul.
The win keeps Toulouse on course for another quarter-final place, leaving them level on 15 points with chief rivals Saracens at the top of Pool 3.
A flu bug disrupted Connacht's preparations as Nathan White and Frank Murphy were late withdrawals from the replacements' bench.
But they made a positive start with Robbie Henshaw and Rodney Ah You carrying with intent, and Parks powered home a penalty from 44 metres out.
Toulouse responded through the boot of Beauxis and used turnover ball to grab the game's opening try, Medard hacking on a kick through from Beauxis and beating Eoin Griffin to the touchdown.
The successful conversion was cancelled out by a snap drop goal from Parks after Toulouse failed to gather the restart. The gap remained at 10-6 as Beauxis slid a scrum penalty narrowly wide.
Connacht had enough territory to cause problems but they could not get their attack firing, and Parks missed a penalty effort from inside his own half.
From the restart, Beauxis created the opening for Medard's second try. The number 10 caught the Connacht defence flat with a pinpoint cross-field kick and Medard muscled past Henshaw's initial challenge to dot down on the left.
Home prop Brett Wilkinson went close from a lineout maul, the Toulouse defence coming under increased pressure before Parks ensured a three-point return with another crisply-struck drop goal.
Right on time, the French side's forwards upped the ante and their power set up strong-carrying hooker Tolofua for a deserved try, following two bulldozing runs from number eight Picamoles.
Beauxis added the extras for a 22-9 lead at the interval as they doused Connacht's fire, showing ruthless efficiency especially with their telling kicks.
The second half was scoreless until Toulouse worked a short 55th-minute lineout, Tolofua linking with Yannick Nyanga who sent Picamoles powering through Fionn Carr's tackle to score in the left corner.
The concession came at the worst possible time for Connacht as Parks' replacement Craig Ronaldson injured his hamstring before the lineout. Academy player Darragh Leader replaced him.
Toulouse's counter-attacking threat was in full view again on the hour when Medard was inches away from completing a hat-trick. Connacht centre Griffin did brilliantly to deny him in a foot race.
Henshaw and Carr threatened briefly for the westerners, however Beauxis' second penalty and a terrific solo effort from halfway from Fickou finished off a satisfying night's work for the four-time European champions.
- Sports & Recreation
- Lionel Beauxis
- Louis Picamoles
- Christopher Tolofua
- Dan Parks