With Hearts winning at home to Dunfermline it kept Rangers within nine points of the league leaders with matches away to Livingston and then at home to Inverness Caley to follow in the coming eight days.
After toiling laboriously in vain for 90 minutes against Artmedia in midweek the irony that it took Rangers only 30 seconds to break the deadlock on this occasion will no doubt not have been lost on McLeish.
And, after telling his star striker to spend more time inside rather than outside the penalty box, the manager probably afforded himself a wry smile as he watched Dado Prso lollop down the touchline to create the goal.
The Croatian wheeled into the box before clipping in a cross that skidded off the head of Lovenkrands and fell kindly for Burke at the back post.
The young winger – starting in place of Hamed Namouchi – needed no prompting to bury the dropping ball past his former team-mate, Graeme Smith, in the Motherwell net.
It was Rangers’ first goal in three matches and they almost had a second 11 minutes later when Julien Rodriguez leapt highest to nod Ross McCormack’s corner beyond the reach of Smith.
Ibrox rose in expectation but Shaun Fagan was in the right place to clear the Frenchman’s looping header off the line to keep Motherwell in the game.
While his fellow attackers queue up for a stint on the Ibrox treatment table, Prso’s greatest attributes remain his durability and indefatigability.
The striker again was a blur of energy, working tirelessly for others down the flanks and posing a menacing threat whenever Burke or Lovenkrands sent crosses into the box.
Three times in the first half he came close to netting his eighth goal of the season, heading a Fernando Ricksen cross narrowly wide, powering in another header that Smith stretched to save before thumping a volley into the stand from a teasing Burke cross close to the break.
From the second of those three chances, Burke was alert to nod the loose ball into the net but, as he whirled away to celebrate, the assistant referee’s flag curtailed the celebrations.
Motherwell, sticking to a rigid 4-5-1 formation even after losing an early goal, posed little sustained threat as an attacking force although still produced a few chances to nick a goal of their own.
Scott McDonald – his name raucously cheered before kick-off following his heroics at the end of last season – curled an effort just wide after seven minutes and then seized on a slack McCormack pass to test Ronald Waterreus shortly before the interval.
It left Rangers in a comfortable position as they trooped up the tunnel at half-time but with a nagging sense that, just as against Artmedia, their inability to convert chances into goals could yet come back to haunt them.
The jittery start McLeish’s men made after the break did little to ease the tension escalating around the stadium, a situation not quelled by a tactical adjustment that saw McCormack replaced by Ian Murray and Lovenkrands asked to perform through the middle alongside Prso.
Burke continued to be Rangers’ most productive outlet but saw his shot – a rarity in a torpid second half – easily held by Smith before Lovenkrands drove an effort against the post after being played in by Prso.
As Ibrox groaned in despair, it would take the genius of the Croatian to put the smiles back on their faces as Rangers finally made the game safe with a second goal just 60 seconds later.
The striker seemed to have worked his way into a cul-de-sac on the edge of the Motherwell box but somehow managed to twist his way past Hammell and Kinniburgh to send an enticing ball across the face of the goal that Lovenkrands poked into an empty net.
The result finally safe, McLeish handed Alan Hutton his first appearance since breaking his leg in February and then also withdrew Prso who left to the loudest ovation of the day.
Few could argue it wasn’t deserved.
RANGERS (4-4-2): 25 Waterreus; 2 Ricksen, 16 Rodriguez, 5 Andrews, 3 Bernard; 17 Burke, 7 Hemdani (Hutton 72), 6 Ferguson, 26 Lovenkrands; 9 Prso (Thompson 76), 44 McCormack (Murray 58)
Subs not used: Klos, Pierre-Fanfan, Malcolm, Namouchi
Booked: None
MOTHERWELL (4-5-1): 15 G Smith; 2 Corrigan, 5 Craigan, 22 Kinniburgh, 3 Hammell; 21 Fagan, 4 Kerr, 9 Foran, 7 Scott McDonald, 11 Paterson (Fitzpatrick 58); 12 Clarkson (Hamilton 78)
Subs not used: Marshall, Steve McDonald, Quinn, D Smith
Booked: None