The Spiders almost got off to a lightning-fast start when Cameron Bruce found himself in space on the left after just 30 seconds with his shot deflected just wide for a corner that was mopped up by the visiting defence.
With five minutes gone Bruce whipped in a cross to the back post where Rocco Hickey-Fugaccia rose and nodded home however an offside flag halted the celebrations.
Livingston threatened for the first time two minutes later when a cross from Samson Lawal found Che Reilly who sent a header flashing wide.
The Lions carved out another chance 11 minutes later when a lightning break teed up Dylan Bahamboula however his shot went high over.
Midway through the opening half a curling forward pass from Zach Mauchin found Liam McLeish breaking into the Livingston box with the striker sending his shot just off-target. McLeish picked up a knock during that move and was replaced on 27 minutes by Kane Thomson.
Queen’s created the next chance as well Hickey-Fugaccia sending a shot thumping against a post only to discover he was flagged for offside a second time.
As the first half entered injury time it looked like Hickey-Fugaccia had worked his way through the Livingston defence however Myles Welch-Hayes got back just in time to clear.
The visitors started the second half brightly and Bruce made a fine clearing header to snuff out an early opportunity with Young Queen’s Park responding with a through ball from Lewis Reid that threatened to release Thomson however the substitute was crowded out.
On 54 minutes Hickey-Fugaccia went on a solo run that took him deep into Livingston territory and when his shot was deflected it looked like Thomson would have a glimpse of goal however an offside flag was again raised to end the danger.
Recently introduced replacements Joseph Smith and Andrew Lind combined with an hour gone with only an outstretched Livingston leg preventing Smith’s cut-back causing danger.
With 20 minutes left Livingston’s Calan Ledingham popped up six yards out and sent a looping header towards the Queen’s goal with Benjamin Ferguson perfectly placed to kick clear just as the ball threatened to go over the line with Reid tidying up the loose ball.
With 73 minutes played goalkeeper Liam Russell picked out Thomson on the left with a clearance and the sub ran 40 yards towards Jack Hamilton’s goal before slipping a pass to Hickey-Fugaccia who saw his net-bound shot pushed hight into the air by the visiting shot-stopper.
Hickey-Fugaccia created the next opportunity as he surged up the park however the winger had to be content with winning a corner that was played to Ricky Waugh at the edge of the box and his chipped effort brought out a fine stop from Hamilton.
In added-on time another raid by Thomson looked to set up a winner however Hamiton stepped in again to keep his goal intact.
Penalties were called for and YQP’s Reid, Thomson and Waugh all netted as did the visiting Welch-Hayes, Bahamboula and Lawal before Hickey-Fugaccia made it 4-3 against his former club.
Goalkeeper Russell then saved from Livingston’s Jason Craig and that allowed Mauchin to step up and find the net to secure an extra point.
Queen’s Park – Liam Russell, Zach Mauchin, Cameron Bruce (Joseph Smith 57) Benjamin Ferguson, Lewis Reid, Ricky Waugh, Rocco Hickey-Fugaccia, Lennon Connolly, Liam McLeish (Kane Thomson 16), Aaron Healy (Andrew Lind 57), Alex Fairlie (Jamie Bradley 77).
Unused substitutes – Archie Graham, Ross McLean.
Livingston – Jack Hamilton, Calan Ledingham, Max Williamson, Samson Lawal, Myles Welch-Hayes, John Binnie (Marshall Boyd 84), Scott Bitsindou (Rudi Bryce 46), Sam Cuthbert (Jason Craig 77), Dylan Bahamboula, Mackenzye Campbell (Corey Kirk 84), Che Reilly (Alex Mann 63)
Unused substitutes – Zach Balfour (G/k).