The defeat ends Sweden's interest at Roland Garros this year, after Goransson was also eliminated in the Men's Doubles earlier today, losing in straight sets alongside Evan King to Harri Heliovaara and Henry Patten. King and Gaby Dabrowski now await Mektic and Muhammad in the Semi-finals.
A match against his partner looked on for Goransson after he and Routliffe battled back to take the first set. They missed two break point chances in the fourth game before losing serve in the seventh after costly mistakes from New Zealander Routliffe.
However, they pounced on double faults from Mektic in the 10th game to break back, then took their chances on Muhammad's serve in the 12th to win 7-5.
The second set came down to the third game, where the Croatian-American duo got the better of decisive long rallies to break Routliffe's serve. Every other game in the set was held fairly comfortably, meaning Mektic and Muhammad took it, 6-4.
After benefitting from a walkover in the previous round, Mektic and Muhammad were certainly fresher than Goransson, playing his second match of the day. The Swede served first in the 10-point tiebreak, and though an unforced error from Routliffe put them on the back foot, a winner from Goransson on a 21-shot rally proved the Rang man was not slowing down yet.
The next three points went with serve before a loss from Muhammad put the Swedish-New Zealander pair 4-2 up, part of a 7-2 run that that put them 8-4 ahead, only for Mektic and Muhammad to score three in a row and make it a one-point game.
Goransson struck to make it 9-7 and put his side on the brink, only for a Mektic backhand to save match point. The Croatian held serve twice to go 10-9 up, before Goransson and Routliffe saved three more match points on the way to making it 12-12.
But a crucial loss of serve from the Swede gave his opponents another chance, and this time a forehand winner from Muhammad following Mektic's serve gave the duo a 14-12 win in the third set, and 5-7, 6-4, 14-12 in the match.
It's a first French Open Mixed Doubles Semi-final for the 37-year-old Croatian after twice getting to that stage twice in the Men's Doubles, while the 35-year-old American will play at that stage for the first time in any Roland Garros event.
For Goransson, this week has seen his best French Open results in the Men's and Mixed Doubles, while two-time US Open Women's Doubles champion Routliffe is yet to bypass the last eight in France.