Nuno Capucho and Michael Ball will take the plaudits for their first-half goals but it will be the combined effort of all of his players that will have most pleased Alex McLeish as he watched on from the visitors’ dug-out.
The sight of his captain Craig Moore easing his way back from injury will also have warmed the heart of the Rangers manager with a make-or-break trip to Parkhead looming on the horizon.
Special mention must also go to Capucho who shrugged aside recent criticism to put in an energetic shift in the centre-forward role in place of Michael Mols.
It was the Portuguese forward who headed Rangers in front with just six minutes gone.
Capucho had already sent one header past the post minutes earlier when he rose highest to send Chris Burke’s pinpoint cross flashing past Julian Speroni.
It was no more than Rangers deserved even by that stage after attacking Dundee from the first whistle, with Bob Malcolm working the goalkeeper early on before Peter Lovenkrands’ tame effort was booted off the line by Dave McKay.
Dundee – fighting literally for their very survival – battled back into the match, with Barry Smith forcing a hat-trick of saves from Stefan Klos before the German goalkeeper made a brave parry from a Nacho Novo effort.
With play raging from end to end, it made for an engaging spectacle, with Novo a particular menace for the Rangers defence throughout an absorbing 90 minutes.
After 35 minutes, the Light Blues doubled their lead with a curious sort of goal. Mikel Arteta was hauled down by Bobby Linn around 30 yards from goal and Ball’s attempted cross evaded everyone and nestled into the corner of Speroni’s net.
Dundee refused to buckle and only the width of the post denied Lee Mair the chance to reduce the deficit just before the break.
With the frame still jangling, Lovenkrands then whacked a left foot effort off the other post as Rangers opened the second period again in the ascendancy.
It was to prove something of a false dawn, however, with the Light Blues largely restricted to a handful of Burke centres that failed to find any willing takers.
Dundee were also less effective in the second period, although proceedings could have turned out differently had Ball not stuck out a leg to halt a rampaging run from Linn.
A late cameo from Christian Nerlinger offered more cheer to McLeish although Rangers should have sealed the win when Capucho beat the offside trap to feed sub Paolo Vanoli who hit his shot straight at Speroni.
DUNDEE (4-4-2): 1 Speroni; 3 Mackay, 6 Wilkie, 19 Mair, 16 Hernandez; 2 Smith, 30 Fotheringham, 18 Sancho (McLean 66), 26 Brady; 33 Linn, 17 Novo
Subs not used: McAfferty, Macdonald, Cameron, Robertson
Booked: Fotheringam (86)
RANGERS (4-4-2): 1 Klos; 2 Ricksen, 3 Moore, 25 Berg, 18 Ball; 30 Burke, 12 Malcolm, 23 Arteta, 26 Lovenkrands (Vanoli 78); 7 Arveladze (Nerlinger 66), 20 Capucho
Subs not used: McGregor, Ross, Ostenstad, Nerlinger
Booked: None
Man of the Match: Craig Moore