Scotland's athletes won 10 medals - four gold, three silver, three bronze - and are third in the medals table in one of the country's best ever starts to a Games.
The haul included a surprise gold for 20-year-old Murdoch, who beat Glasgow-born favourite Michael Jamieson in the 200m breaststroke as he broke the Commonwealth Games record at Tollcross International Swimming Centre. Jamieson won silver.
Earlier, Miley, from Inverurie, Aberdeenshire, scored an emotional triumph in the 400m individual medley, where she also smashed the Commonwealth record in defending her title won in 2010 in Delhi.
The 24-year-old wrapped herself in a Saltire flag to complete a lap of honour before a cheering home crowd. She then broke down in tears as she stood on the podium to hear Flower Of Scotland ring out in the arena.
Scotland's first gold medals were won in the judo, with Edinburgh sisters Kimberley and Louise Renicks winning the under-48kg and under-52kg classes respectively. Stephanie Inglis claimed silver in the women's under-57kg.
Team Scotland chiefs said it had been a "historic and proud day" for the home nation.
But the real winners were tens of thousands of fans who flocked to sporting events across the city, and thronged the route of the men's and women's triathlon events at Strathclyde Park, near Motherwell.
The heatwave, which saw conditions reach 26°C (79°F), only contributed to the atmosphere at the Friendly Games. Glasgow city centre was thronged with sports fans enjoying the vibe as shops, bars, restaurants and other traders enjoyed the benefits of the influx of tourists.
The other medals for Scotland were gained in the Sir Chris Hoy Velodrome, where para-cyclists Aileen McGlynn and Louise Haston won silver, while there were bronze medals for judo stars Connie Ramsay, veteran John Buchanan and James Millar.
However, Murdoch's success just after 9pm was one of the major talking points of the first day's action. His win stunned the crowd and, as his ecstatic parents waved national flags in the stand, even Murdoch said he could not believe he had triumphed.
He said: "There is no way that just happened. In the last 100m the sound was just amazing and it drove me on. I felt really good this morning in the heats, but I didn't believe I could do that. It is my grandad's 70th birthday so that is for him."
Jamieson, who had been tipped to win, said: "I don't prepare to come second and it's just not good enough for me."
Day one was also the first serious test of Glasgow's transport infrastructure, which is under pressure to cope with about 300,000 extra journeys per day.
ScotRail reported minor disruption as passengers faced a handful of cancellations and some services skipping normal stops to reduce congestion on the lines.
Malcolm Roughead, chief executive of tourism agency VisitScotland, said: "An estimated one million spectators are here for the Games. These visitors, whether here for the day or longer, help contribute to Scotland's economy by using restaurants, drinking in bars or shopping in retail outlets."