Wanderers trailed to Kieron Dyer's eighth-minute strike and could have been in even deeper trouble as the Magpies made an excellent start.
However, keeper Pavel Srnicek, making his first start for Glenn Roeder's side since October 1997, got himself into a tangle with Peter Ramage on 32 minutes which saw the defender head into his own net to drag Bolton back into the game.
Sam Allardyce's half-time teamtalk seemed to do the trick and his side needed only 12 minutes to get their noses in front, former Newcastle target Anelka slotting home at the far post after El-Hadji Diouf had sliced across goal.
The Frenchman's strike handed the home side a fourth successive Premiership win as the Magpies tasted defeat for only the second time in seven attempts in front of a crowd of 26,437.
But while Bolton were vastly improved in the second half, the visitors headed back across the Pennines knowing they should perhaps be doing so with something to show for their efforts and having contributed to their own downfall.
Newcastle arrived at the Reebok Stadium with five wins in their last six Premiership games, but with injuries still forcing Roeder to change his plans by the game.
Shay Given's groin problem meant Srnicek got his chance, although that was perhaps expected after the Irishman's premature departure during Saturday's 3-1 win over Tottenham.
However, Nolberto Solano's absence with a similar problem handed a debut to 19-year-old David Edgar, son of former Magpies keeper Eddie, at right-back.
The prospect of launching a senior career in the company of the likes of Anelka and El-Hadji Diouf may have made for a sleepless night for the youngster in a back four with an average age just slightly above 20.
However, for 32 minutes Edgar and his team-mates thoroughly enjoyed their Boxing Day test.
That was due in no small part to the fact that Dyer fired them in front within eight minutes of kick-off, capitalising on a careless defensive header by striker Kevin Davies to sprint into the box and fire past the helpless Jussi Jaaskelainen.
Obafemi Martins might have doubled his side's lead on 17 minutes when he blasted a left-foot drive beyond the keeper's dive but just wide of the far post, and James Milner threatened on more than one occasion as Bolton looked repeatedly vulnerable at the back.
Despite enjoying a more than healthy share of the possession, the home side struggled to create much of any note even with Anelka and Diouf concentrating on Edgar, who was ably assisted by Scott Parker and Nicky Butt ahead of him.
But just as the visitors started to anticipate a pat on the back from their manager they shot themselves in the foot, and it was the elder statesman who had to shoulder the blame.
Ramage waited until he could wait no longer for Srnicek to come for Gary Speed's hopeful header into the box and, with Kevin Nolan bearing down on him, the defender tried to head the ball back to his keeper but succeeded only in putting it into his own net.
Ivan Campo volleyed over from a 42nd-minute Anelka cross as Bolton staged a late flurry, but both sides left the pitch on the whistle with mixed emotions.
Roeder was nothing if not positive at the break, asking Dyer to push on alongside Martins and Antoine Sibierski in a three-man frontline.
However, it was Bolton who were quicker into their stride with Edgar once again the man under pressure, and the breakthrough arrived just 12 minutes into the half.
Davies flicked on Ivan Campo's long throw and when Diouf scuffed a shot across the face of goal, Anelka arrived at the far post to slam the loose ball into the net.
Srnicek's uncertainty was causing panic at the back and although he got a punch to Diouf's 61st-minute free-kick, he needed help to complete the job.
Nolan might have made it 3-1 with a 77th-minute flicked header, but the visitors were preparing a late assault of their own.
Substitute Giuseppe Rossi poked a shot into Jaaskelainen's arms and fellow newcomer Emre, on for Dyer, sent a dipping long-range effort just over in quick succession.
But it was Butt who went close six minutes from time, forcing the keeper into a diving save with a shot from distance as Roeder's men battled all the way to the whistle, but did so ultimately in vain.
