A dramatic day of action in the German Masters qualifiers saw two 147 breaks being compiled at the Metrodome in Barnsley.
The perfect breaks came within minutes of each other, with Carter compiling his second career 147 in his 5-0 whitewash win over Wang Yuchen.
Shortly after on a nearby table, Scotland’s Muir recorded his maiden max in beating Itaro Santos 5-2.
It marks as the seventh and eighth 147 breaks of this campaign – 11 were constructed during the 2011/12 season.
Additionally, it was just the second occasion the impressive feat had been achieved twice in the same day.
Strangely, Carter and Muir now meet each other in the second round with a place in Berlin at stake.
Thursday’s play had a mixture of the first round and the final hurdle as the preliminary stage began its conclusion.
Ronnie O’Sullivan was among those to already book his spot on the flight to Germany after a 5-3 victory over Gary Wilson.
The 2012 champion raced into a 4-0 lead only to see his opponent fight back with runs of 78, 73 and 93.
A 94 from the ‘Rocket’ ensured his safe passage into the last 32, where he won’t be joined by John Higgins after a shock defeat for the Scot.
Higgins, who won a pair of lucrative invitation tournaments in November, managed just a solitary frame in response to a great triumph for talented Chinese teenager Zhao Xintong.
Stephen Maguire and Michael White avoided such upsets by narrow margins, each prevailing 5-4 in tight affairs with Noppon Saengkham and Liam Highfield respectively.
Northern Ireland Open champion Mark King qualified as well, winning the last three frames with an aided run of 113 to see off Andrew Higginson 5-3.
It was easier for the defending champion Martin Gould, who recorded a 5-1 defeat of Craig Steadman, which was the same margin in which Ricky Walden enjoyed success over Robbie Williams.
Similarly, Dominic Dale comfortably overcame Alex Borg 5-1.
Earlier in the day, the likes of Mark Selby, Stuart Bingham, Neil Robertson, Mark Allen, Mark Williams and Judd Trump all emerged victorious from their last 128 ties.
The latter could have made a 147 break of his own, only to miss the final red in the last frame of his 5-0 drubbing of Paul Davison.
The German Masters qualifiers concludes on Friday.