The Magpies had taken only two points from their previous six games while Bolton's victory over Blackburn in midweek ended a run of five straight defeats, and in the first half it appeared very much a battle between two struggling sides.
But the deadlock was broken in the 69th minute when Ben Arfa netted his first goal in more than a year and the prolific Ba doubled the lead soon after.
Defensive woes have been the problem for Newcastle boss Alan Pardew, who was able to call on centre-back Mike Williamson for the first time since he suffered an ankle injury in August.
Yohan Cabaye was back after suspension, while for Bolton Marcos Alonso and Gretar Steinsson were unavailable so Paul Robinson and Dedryck Boyata came in.
If fans were hoping for a Boxing Day treat they certainly did not get it in the first half as both sides struggled to string passes together.
There were only two chances of note, one for either side, in almost identical circumstances.
Newcastle dominated the early stages and in the 14th minute Ryan Taylor drew a good save from Jussi Jaaskelainen diving low to his left with a free-kick after Fabrice Muamba had fouled Cabaye 25 yards out.
Bolton's confidence levels did not seem to have been improved by Tuesday's win but they gradually came into the match and were close to taking the lead six minutes before half-time.
Cabaye was harshly penalised for a nudge on Nigel Reo-Coker just outside the box and Martin Petrov's free-kick was heading for the bottom corner until Tim Krul thrust out a hand.
Leon Best had the final chance of the half when he was picked out by Ryan Taylor's corner but he could manage only a glancing header and guided the ball well wide.
Bolton's season was summed up by a sequence of play in the 55th minute. First Robinson found Ngog with a good ball down the left and Klasnic eventually picked up the striker's cross-shot only to trip himself up as he looked to get a shot away.
At the other end, Jaaskelainen blocked an effort from Gabriel Obertan before Newcastle made the first substitution of the afternoon, Ben Arfa coming on for Best.
Bolton were certainly looking more of a threat going forward and Petrov lashed an effort just wide of the far post.
But in the 69th minute they went behind as Newcastle at last put together a move of real quality, ending with Taylor crossing for Ben Arfa to crisply volley in only his second goal for the club and his first since September 2010, shortly before he suffered a broken leg against Manchester City.
And two minutes later the game was all but over as poor defending from Paul Robinson let in Obertan down the right and his cross was clipped in by Ba despite the best efforts of Gary Cahill.
It was Ba's 14th goal of the season, and he almost added another moments later but this time Jaaskelainen was quickly off his line to block, Taylor then fired a free-kick well over the bar.
Bolton boss Owen Coyle threw on strikers Tuncay Sanli and Kevin Davies but it was already a lost cause and even a consolation was beyond the Trotters.
Boos rang out at the final whistle, with the result meaning Bolton stay three points from safety and now only one point above bottom side Blackburn.