The world number 52 walked into the York Barbican to the sound of Babylon by David Gray, a piece of music chosen in memory of his father, Hector, who died in early October.
The moment appeared to catch him unexpectedly, although once the match settled, he imposed near-total control on proceedings.
"Snooker is a game at the end of the day, it's not life or death," Donaldson told the BBC after the match.
"With what I have been through, I can tell you what's important and what's not important. When the pressure is coming on, I just tell myself 'it's a game of snooker' and get on with it.
"I was fine until I got to the top of the stairs - and the last time I was in this venue was with my dad. It was good emotion though.
"Tough to go through but once I got the first frame, after that I was all right."
Having edged through qualifying by overturning a 5-0 deficit against Stuart Bingham, the Scot arrived in the main draw with obvious momentum, and it showed.
The 31-year-old built a 3-0 advantage through disciplined safety and patient scoring, despite admitting that maintaining focus early on had been difficult.
Allen no match for Donaldson
Allen, champion here in 2022, briefly halted the surge by taking the fourth frame and appeared to be settling into the match.
Yet the contest soon became defined by protracted tactical passages, including an hour-long frame and another of roughly 50 minutes. These suited Donaldson far more than the Northern Irishman, and he ultimately continued to win the key exchanges and closed out the match with authority.
Allen, the highest-ranked player to fall in the first round so far, offered a blunt assessment.
The 39-year-old suggested he had prepared well, felt ready, yet simply found himself outplayed.
"It took a big character to continue playing and all credit to Scott with everything he has been through," he said after the loss.
"It looked like he was giving everything on every shot."
Zhang through and Ronnie arrives
There was further tension elsewhere in the arena as Zhang Anda edged Gary Wilson 6-5 in the tournament's first decider of the week. Wilson appeared in command after breaks of 58, 52, 65 and 91 helped him into a 5-3 lead.
Zhang, however, recovered with admirable calm, taking the final three frames to complete the turnaround.
His reward is a meeting with reigning world champion Zhao Xintong, who dismissed Long Zehuang 6-1 in the afternoon session.
The action continues in York on Tuesday, with favourite Ronnie O'Sullivan hitting the table against Zhou Yuelong and Mark Selby facing Lei Peifan in the afternoon session.
Kyren Wilson faces Elliot Slessor and Barry Hawkins takes on David Lilley in Tuesday's evening session.
