The Senegal international scored twice inside three first-half minutes to give his side a commanding lead, and then after Junior Hoilett had pulled one back for the visitors, who had Martin Olsson sent off, headed home a third with 54 minutes gone.
Alan Pardew's men might have won even more comfortably with Leon Best passing up two late opportunities to add to his three goals for the season, but they were good value for a win which took them to 12 points from a possible 18 and stretched their run to eight games without defeat in all competitions during the current campaign.
In the process, they ended Blackburn's remarkable run of five successive Premier League victories at St James' Park on an afternoon when they never looked like adding to it in front of a crowd of 46,236.
The two sides will meet again in the Carling Cup fourth round at Ewood Park next month after being paired together in today's draw, but the Magpies will head to Lancashire brimming with confidence after cementing their place in the upper ranks of the league table.
There was much anger and frustration on Tyneside when the summer transfer window closed with the club having failed to land the high-profile striker for whom they had been searching since Andy Carroll's departure in January.
Amid the fall-out, however, Ba's arrival had gone largely unnoticed after an uncertain start to his career at St James'.
But today was the day the 26-year-old chose to announce himself in style with a treble which reminded the locals of the potency which brought him seven goals in just 12 Premier League appearances for West Ham last season.
Ba whistled a long-range sixth-minute effort over Paul Robinson's crossbar as the Magpies made a bright start with Gabriel Obertan particularly influential.
But he demonstrated his prowess in front of goal 21 minutes later when he opened his account in some style.
Best's driven cross from the left presented its own challenges, but Ba controlled superbly to turn central defender Scott Dann and smash a right-foot shot past Robinson.
The striker dropped to the ground to kiss the turf, and he was celebrating again within three minutes.
Steven Taylor, who had headed upfield for an earlier free-kick, was still deep in enemy territory to head Danny Simpson's deep ball back across the penalty area and Olsson could only help it on towards Ba, who headed it past the stranded Robinson from close range.
That really should have been it for the Magpies, who had dominated for much of the opening half-hour, and they might have added to their lead had Dann not made an important block to keep out Jonas Gutierrez's 36th-minute shot.
However, Rovers got themselves back into the game seconds later after Ryan Taylor had gifted them possession on halfway.
Mauro Formica capitalised and the ball was fed out to Olsson on the left, and he crossed for Hoilett, who had looked the visitors' most dangerous player, to control and thump a half-volley into the roof of the net.
Pardew was furious on the touchline, although his mood might have improved on the stoke of half-time had Obertan's shot flown inside rather than outside the post after he and Yohan Cabaye had staged a pacy counter-attack.
Rovers returned in spirited fashion and went close when Olsson met Michael Salgado's 53rd-minute cross and looped a shot on to Tim Krul's crossbar.
But the Magpies eased further ahead within seconds when Ba looped a header over Robinson and into the net with Best desperately trying to get the final touch.
Simpson was almost caught out by Olsson once again on the hour when he failed to intercept another Salgado cross, but the ball hit the midfielder's shins and dropped wide.
Obertan curled a 68th-minute shot just wide with Newcastle dominant once again, and they caused was aided further two minutes later when Olsson was dismissed after being booked for the second time for a cynical challenge on Best.
Cabaye tested Robinson from distance and Best twice fired over the top after working himself into promising positions.
David N'Zonzi launched a dipping long-range effort over Krul's bar with eight minutes remaining, but Rovers' cause was forlorn.