Jerome Rothen got the ball rolling after just two minutes when he took advantage of a weak Manuel Pablo back header to lob home expertly past the stranded Francisco Molina.
After Flvio Roma had the n denied Sergio with a flying stop from 15 yards, the hosts doubled their lead when Ludovic Giuly sprung the Depor offside trap before rounding Molina to tap home into an empty net.
Prso, only starting in the absence of the injured Fernando Morientes, opened his account for the evening with two goals in a four minute spell just before the half-hour mark, firstly rising unchallenged to head home a left-wing Rothen corner, before nodding in at the far post following Givet's headed cross.
The visitors threatened to find a way back into the game however with two quick goals of their own.
Spanish international Diego Tristan reduced the arrears, controlling a Jose Amavisca cross before swivelling sharply to fire low left-footed past Roma, and Leonel Scaloni then followed up to tap home after the keeper had parried a Juan Carlos Valeron shot into his path.
Unbelieveably, however, the first half action was not over, and Prso completed his hat-trick when Giuly toed past the onrushing Molina to allow the Croat to roll into an empty net from 12 yards.
Depor opted to bring on substitute keeper Gustavo Munua at the interval but the Uruguayan fared no better than Molina, and just two minutes into the second period was picking the ball from his net when his headed clearance fell invitingly to Jaroslav Plasil who lofted home delightfully from 30 yards for Monaco's sixth.
With Depor in utter disarray Rothen broke down the left flank just a minute later to square for the onrushing Prso to lash home for his fourth via a slight deflection of Romero.
Tristan notched his second of the night just before the hour mark when he beat two defenders before scooping home delightfully over Roma, but Monaco weren't to be outdone and number eight arrived courtesy of former Edouard Cisse who held off a couple of flimsy challenges before lashing home left-footed from 25 yards.
The amazing win, a UEFA Champions League record, takes the French outfit back to the top of Group C two points ahead of Depor who lost their unbeaten record in the process.
