Bruce Anderson tucks home the third after just 21 minutes
Mark McGhee "couldn't believe" his eyes as "diabolical" defending saw his first home game as Dundee manager end in a humiliating defeat to Livingston.
Three goals in the first 21 minutes by Bruce Anderson - twice - and Scott Pittman had Dundee fans leaving early.
Jack Fitzwater completed the rout to leave Dundee anchored to the foot of the Scottish Premiership, nine points from the safety of 10th place.
"I couldn't believe what I was seeing," McGhee said.
"To be 3-0 down with the resolute side that we thought we were putting out was bamboozling really. Today we saw why we're bottom of the league."
As bad as Dundee were, Livingston excelled as they pushed themselves into the top six.
They started how they meant to go on. After only three minutes, Alan Forrest ghosted to the bye-line. His cut-back was palmed straight to Anderson, who was more than happy to gobble up the chance presented to him.
The hosts' statuesque defending was further punished when Joel Nouble collected on the right, danced by Cammy Kerr and fired low into the box. This time Pittman was standing in wait to tap home from close range.
Dundee didn't learn from their previous two lessons. Forrest, instrumental once again, played a quick free-kick into the path of Nicky Devlin, who squared to Anderson, running in front of his man to fire in a third.
Just 21 minutes had been played and Dundee were three goals behind. Their fans were heading for the exits. Zeno Ibsen Rossi was made an example of, hauled off in place of Paul McMullan.
Livingston could have made the scoreline even more impressive, with Ayo Obileye, Andrew Shinnie and Pittman all going close. The latter had the ball in the net at another point, only for the offside flag to deny the visitors another goal.
The only chance that might have got McGhee out of his seat in the stands fell to Ryan Sweeney before half-time, but Max Stryjek was right behind that header. It was all the Polish keeper had to do all afternoon.
After the hour mark, Livingston finally got their fourth. Forrest's corner was headed off the line and back to him, but the winger played it back to Fitzwater, who showed good composure to take a touch, get his head up, and curl into the back post.
Those plucky Dundee fans who had remained, now made for the exits. When they had not been silenced by the visitors play, they were booing their own team's display. And who can blame them.
Man of the Match - Bruce Anderson
The striker's predatory instincts have really come to the fore this season. That's 11 league goals now
What did we learn?
If McGhee was an unpopular appointment, his approval ratings might now be unrecoverable after just two games. It's hard to see what the new manager can possibly do to stop his side hurtling towards the Premiership trap door.
The leakiest defence in the league, they looked devoid of any confidence when being attacked directly. Up top, they created very little and Zak Rudden was largely anonymous before he was subbed off.
The travelling Livingston fans, meanwhile, were delighted. They have a very tough run of fixtures coming up - Dundee United, Hearts and Celtic - but can take every confidence from this performance.
Forrest is on a superb run of form, notching two assists and setting up another with his quick thinking. His contract is up in the summer and teams higher up in the league will almost certainly be sniffing around him.
What did they say?
Dundee manager Mark McGhee: "That first twenty minutes was diabolical. We were brought here because there was something broken. It wasn't going to be fixed in a week.
"The fans have every right to feel the way they felt today and give the team stick. We will work hard to show them that we are better than that.
Livingston manager David Martindale: "It was a fantastic performance. Without being disrespectful, it was done in the first 30 minutes.
"It's well deserved. We were written off at the start of the year by nearly everybody. Now we're sitting top six, I think it's remarkable. The boys deserve massive credit."
What's next?
A hectic run of fixtures awaits Dundee, with the first test a midweek visit of Hibernian on Wednesday. Meanwhile, Livingston host Dundee United (both 19:45 GMT).
