The Senegal international, who arrived from Manchester United earlier this month, marked his full Rovers debut by heading the opener in the 29th minute.
The 22-year-old also hit the crossbar from close range after the interval before stabbing home his second 11 minutes from time and nodding in a third before Jens Berthal Askou’s 90th-minute consolation.
Manager Sam Allardyce had given his loan star two substitute outings in the Premier League but chose tonight’s cup fixture against npower Championship opposition to give him his first start and he did not disappoint.
Diouf, who made six appearances for United last season and also sat on the bench for their Carling Cup final win over Aston Villa, was heavily involved from the outset.
In the 10th minute the striker, standing on the penalty spot, had a wild swing at a loose ball but failed to connect but when it did finally drop to a team-mate in the penalty area Gael Givet drove straight at goalkeeper Declan Rudd.
Brett Emerton’s cross to the far post was a touch too high for Diouf, who in Rovers’ next attack headed down for Amine Linganzi to volley into the floor and take a deflection wide.
Rudd was called into action again when he saved well after Morten Gamst Pedersen directed a downward header goalwards from Emerton’s cross.
Midway through the first half Norwich created their first half-chance but Grant Holt’s header from George Francomb’s inswinging free-kick was comfortably saved by Rovers goalkeeper Mark Bunn.
But the Canaries could not keep Diouf quiet for long and he opened the scoring in the 29th minute with a typical poacher’s goal.
Pedersen’s long throw was flicked on by Christopher Samba and Diouf popped up at the far post to plant a stooping header into the net.
Chances were at a premium for Norwich so David Fox’s shot over the crossbar when unmarked 14 yards out five minutes before half-time was more than disappointing.
Just before the break the visitors’ best opportunity saw Simeon Jackson’s low shot tipped around his right-hand post by Bunn.
Six minutes into the second half Holt saw his shot fumbled by Bunn but he recovered and almost set up the second goal when Diouf beat the onrushing Rudd to a long punt forward.
The Senegal international headed past the Canaries goalkeeper but also wide of the empty net, receiving a blow to the face for his effort.
Just when it appeared Norwich were running out of ideas Holt flashed a near-post header across goal from Fox’s corner and Bunn produced a reaction save to keep the ball out.
Linganzi almost extended Blackburn’s lead when he volleyed against the foot of Rudd’s right-hand post with the goalkeeper beaten in the 74th minute.
And Diouf should have scored seconds later but he planted a close-range header against the crossbar from Pedersen’s left-wing free-kick.
But when Pedersen’s shot from Junior Hoilett’s cross was spooned up in the air by Rudd Diouf stabbed home despite the best efforts of the Norwich defence to prevent it crossing the line.
And Diouf capped a fine individual performance with a five-yard header for his third in the 84th minute.
Berthal Askou’s 90th-minute header was little consolation for the visitors.