The 21-year-old, a veterinary student at Glasgow University, came home third in a quick heat won by Kenya's World Championship bronze medallist Hellen Obiri in a Games record of four minutes 04.43 seconds.
Muir, who broke the Scottish record earlier this month to go fifth on the British all-time list and is ranked eighth in the world, looked comfortable throughout, biding her time before moving up to second at the bell and, safe in the knowledge she had done enough with the top four going through automatically, easing off in the final 30m.
She came home in 4mins 05.19secs, with Hannah England, England's former World Championship silver medallist, joining her in Tuesday's final, finishing one place further back.
Laura Weightman, who is trained by Steve Cram, will also be there after finishing strongly to come home third in the second heat in 4:08.58, while Jemma Simpson made it three Englishwomen in the final, qualifying as a fastest loser.
Muir admitted the pace of the race took her by surprise, but was happy with the run.
"That was quick," she said. "That was quicker than I thought it was going to be.
"It was just a matter of getting around as comfortable as possible and save as much as I can for tomorrow.
"I think I did that today so I am pretty happy."
Muir got the biggest roar of the morning from the near full house and, asked about her reception, said: "It is absolutely amazing. It feels like a Mexican wave of cheers when you go around.
"It is amazing. Usually I can pick out my mum and dad quite easily, but I'm not sure I can with all the flags here."
Kirani James, the Olympic 400m champion from Grenada and one of the biggest names in Glasgow, looked in imperious form in qualifying, less than a month after he became the fifth fastest man in history over the distance.
The 21-year-old, who clocked 43.74 in Lausanne at the start of July, was able to ease off the gas with more than a quarter of a lap to go to cross the line in 45.52, with Michael Bingham behind him in second in 45.80.
Martyn Rooney was a comfortable winner of his heat in 45.57, but England's third entrant, Nigel Levine, had to rely on a fastest loser spot to progress to the semi-finals after coming home fourth in 46.35.
Rooney said: "That was my best race of the year. I will treat the semi like a final."
English trio Christopher Baker, Martyn Bernard and Tom Parsons, along with Scotland's Raymond Bobrownicki qualified for the high jump final, while England's John Lane lay second and Ashley Bryant third after three events of the decathlon.