Cardiff opened up a 2-0 lead in the space of two minutes through Aron Gunnarsson and Don Cowie but Murray offered the hosts hope with a successful 52nd-minute penalty.
And the 28-year-old striker equalised 10 minutes later before completing the dramatic comeback with his second penalty of the match on 72 minutes.
Gus Poyet's Brighton opened up a two-point lead at the summit of the Championship table after downing 10-man Millwall 2-1 at The Den.
Ashley Barnes fired home the opening goal on 17 minutes before Adam El-Abd made it two, five minutes into the second half.
Chris Wood, on loan from Premier League side West Bromwich Albion, pulled a goal back but it proved nothing more than a consolation.
Wolverhampton continued their push for an immediate return to the Premier League with a comfortable 2-0 win at Peterborough.
Sylvain Ebanks-Blake and Bjorn Sigurdarson struck in each half to move Wolves into fifth position and condemn Darren Ferguson's team to their seventh successive loss of the season.
Newly promoted Charlton piled more misery on Ipswich after they recorded a 2-0 win.
Ipswich had a number of chances to take the lead in the first half but were made to pay in the second as Johnnie Jackson tapped home the opener on 48 minutes before veteran striker Ricardo Fuller doubled the visitors' advantage just minutes later.
Jason Scotland reduced the deficit almost immediately however Charlton hung on for victory and increased the pressure on manager Paul Jewell.
In other results on Saturday, Leeds ended Nottingham Forest's unbeaten start to the season with a 2-1 win at Elland Road, while Mark Davies netted a 65th-minute winner as Bolton prevailed 2-1 on their trip to struggling Sheffield Wednesday, who have now lost four games in succession.
A brace from Charlie Austin, including an 89th-minute goal, inspired Burnley to a last-gasp 2-1 victory over Derby Country, while Watford and Bristol City played out an exciting 2-2 draw.