Ali Carter racked up two wins and a draw to qualify for Stage Two at the Championship League but Irish duo Leo Fernandez and Aaron Hill missed out on joining him in the next round.
Two-time World Championship runner-up Carter began his day with a 3-1 win over Michael Georgiou in Group 19.
He then secured qualification by beating Sydney Wilson 3-0 before enjoying a knockabout evening showdown with Dominic Dale, which finished 2-2.
In an interview posted to the Championship League Snooker's Twitter account, Carter said: "Winning the two matches meant the last one to me didn't mean anything. It was a bit of a comedy show at the end but the job was done.
"I've got some goals for this season which I haven't had for a long time so I'm going to try and apply myself properly. I still think I can compete at the top level."
Limerick native Fernandez and Cork teenager Hill, who famously beat six-time world champion Ronnie O'Sullivan at the European Masters last September, missed out on Stage Two however with both finishing second and third respectively in Group 23 behind Switzerland's Alexander Ursenbacher.
Fernandez and Hill both beat Scotland's Scott Donaldson and lost to Ursenbacher, while Fernandez was the victor in their all-Irish head-to-head in a 3-0 win.
The 1997 world champion Ken Doherty is scheduled to take part in Group 14 on 26 July where the Dubliner has been drawn against Jamaica's Rory McLeod and English duo Martin Gould and Ryan Davies.