Marc Libbra and David Zitelli were on target as Hibernian continued their build-up to the Scottish Cup final with a 2-0 victory at Dens Park.
But Dundee manager Ivano Bonetti will be bitterly disappointed at the way his side capitulated in the second half.
Exciting moments were few and far, but the win completed a clean sweep for Hibs, who have won all four League meetings with Dundee this season.
After a quiet opening spell, Dundee went close in the 15th minute with former Hibs centre-back Steven Tweed seeing his powerful, six-yard header cleared off the line by Stuart Lovell.
Claudio Caniggia, returning to the Dundee side, nearly scored in the 33rd minute after bursting through the Hibs defence, but his right-foot shot went a yard wide.
The outstanding first-half moment came in the 37th minute, and it demonstrated the promise Dundee keeper Jamie Langfield possesses.
Langfield brilliantly pushed away Libbra's superb header for a corner, vindicating Bonetti's decision to persist with the young Scot instead of Italian Marco Roccati.
The fans had to wait until the 55th minute for the breakthrough, but it was well worth the wait.
Hibernian's recent recruit Frederic Arpinon chipped a precise pass over a cluster of Dundee defenders into the path of Libbra, and the on-loan striker from Toulouse made no mistake, smashing the ball into the corner of the net from 12 yards.
Dundee survived a penalty claim two minutes later after Walter Del Rio's clearance hit the arm of Tweed but referee David Somers waved play on.
The home side's only really threatening moment came in the 61st minute, when comeback striker Fabian Caballero worked his way into the danger zone but his final attempt was smothered by Nick Colgan.
Hibs secured victory with a 66th-minute second goal. Zitelli took advantage of Barry Smith's slip after the luckless defender had failed to deal with a long ball down the middle from Matthias Jack.
With victory assured, Hibs manager McLeish withdrew both French strikers to offer Mixu Paatelainen and Gary O'Connor the chance to prove their worth ahead of the cup final.