The thumping from Celtic they had anticipated duly materialised and very few travelled south to expose themselves to it. A predictable rout unfolded, albeit Dundee were only a goal behind and competitive until Matt Lockwood was sent off early in the second half, after which they collapsed.
Dundee came under a barrage of criticism from their supporters for replacing Barry Smith with John Brown as manager for the rest of the season, and the weekend filleting of the club was completed by a Celtic team now 21 points clear in the Clydesdale Bank Premier League and only five victories away from being confirmed again as champions. They were so comfortable they won despite clicking only in the second half, during which James Forrest, Dylan McGeouch, Joe Ledley and Gary Hooper added to Ledley's early opener.
Ledley is out of contract at the end of next season and Lennon is eager to open talks with him soon about an extension. On this performance it is easy to see why.
Dundee were game, but playing for 40 minutes with 10 men made defeat inevitable as Celtic took to 23 their total of goals in the last five home league games. "It was Jekyll and Hyde," said Neil Lennon, the Celtic manager. "In the first half we weren't great, in the second half we were excellent."
Brown sat in the directors' box and could at least feel warmed by elements of Dundee's first-half performance. At times their moves and brief spells of pressure sent ripples of complaint around the home stands and they created a handful of decent chances.
Gary Harkins, slow but blessed with skill, made a nuisance of himself. His free-kick squirted into the net only for the goal to be disallowed because John Baird had strayed offside, much to the relief of Fraser Forster who had been too easily beaten. Forster later reacted to tip a deflected Harkins shot over the top before the Dundee man hit the crossbar from the resultant corner.
Parkhead did not like that. Neither did it appreciate Efe Ambrose's dithering to allow Brian Easton through on goal before being crowded out. Ambrose, at right-back, was hooked just before half-time. "Efe looked a bit fatigued," said Lennon. "He's had a lot of football and needs a break. He knows his football wasn't great today but we know he's a good player."
Victor Wanyama had been rested at kick-off, one of a handful of senior men absent from the starting XI, but came on for Ambrose. Georgios Samaras was on the bench but unused, while Charlie Mulgrew, Kris Commons and Scott Brown were unavailable through illness or injury.
Forrest started on the left and McGeouch on the right as Celtic attempted to stretch Dundee from wide. They had little success until Lockwood's red card. Thomas Rogne and Anthony Stokes, both playing for their Celtic futures in the coming weeks, started. The league is mundane for Celtic now but in two days they face Motherwell away, St Mirren in the William Hill Scottish Cup on Saturday and Juventus in the Champions League next Wednesday.
They went ahead with a goal cheaply conceded by Dundee. Emilio Izaguirre sent in a mild cross from the left and Rab Douglas should have done far more than simply parry the ball straight to Ledley's feet. Celtic's captain for the day had a simple finish to drill the ball into the net. It was a horrible moment for Douglas on what may be his final appearance at the home of his former club.
Celtic's latent superiority meant Dundee were constantly vulnerable even in the first half, of course. Hooper blazed one effort over then came much closer with two excellent attempts, the first pushed away by Douglas, the second inches wide. He would surely have had a goal at the start of the second half had he not been held back by Lockwood as he tired to meet Forrest's diagonal pass into the goalmouth. It amounted to the denial of a clear goalscoring opportunity by Lockwood and an inevitable red card and penalty from referee Kevin Clancy. Lockwood, brought on at half-time and sent off in the 49th minute, had not been on long enough to dirty his strip. Forrest tucked home the penalty and suddenly Dundee were in desperate trouble.
The routine completion of Celtic's 16th win in the 18 meetings since last losing to Dundee, in 2001, came when Stokes crossed for McGeouch to score with a fine header back across goal and inside the post. Dundee found it impossible to cope and it was too easy for Celtic when Stokes jabbed a short pass across the box to Ledley, who lifted a shot into the net for the fourth.
When Ledley put a cute ball over the top of the Dundee defence with 10 minutes left it got the finish it deserved from Hooper, who expertly controlled it before burying it beyond Douglas.
"It's been a very difficult week for everybody," said Ray Farningham, the Dundee coach. The Parkhead mauling is over, but Dundee's problems continue. Brown today begins his battle to win acceptance.