Goals from El-Hadji Diouf and Stelios Giannakopoulos piled the misery on Souness, who at this alarming rate of decline will need more than Michael Owen to save his job.
Newcastle and Souness have taken just one point from their opening three matches, one less than at the same stage last season under predecessor Sir Bobby Robson who was eventually sacked before August was out.
The Scot could easily follow, particularly with Manchester United next up at St James' Park on Sunday, and currently with two strikers in form in Ruud van Nistelrooy and Wayne Rooney.
With Newcastle also drawing a blank for the third successive Premiership game, there is no doubt Souness desperately needs a player of Owen's calibre as his side continue to underachieve.
Owen's preferred option, if all else fails at Real Madrid and if Liverpool fail to make the move he hopes for, is to join Newcastle on a season-long loan - and that would appear to be the safer option for the England international striker should the Magpies prove to be his escape route from Spain.
The Magpies are currently a shambles of a side, lacking in imagination and inspiration, and that could ultimately prove the downfall for Souness as he has players of quality in the squad but is currently unable to draw the best from them.
Bar one third minute chance for Lee Bowyer, United struggled for the remainder of the opening half as Bolton pressed, worked together as a unit and ultimately gained their reward.
In truth, Bowyer was a shade unlucky as former Magpie Gary Speed just happened to be in the right place at the right time to head the midfielder's left-footed drive off the line, with Jussi Jaaskelainen well beaten.
It was also Newcastle's best-worked move of the half, involving Amdy Faye, Celestine Babayaro and captain Alan Shearer whose far-post knock down found Bowyer with his back to goal before he cleverly worked the opening.
Bolton soon countered, with captain Jay-Jay Okocha driving narrowly over from an acute angle, while referee Rob Styles was unmoved to the penalty claims of Diouf when he took a tumble on the edge of the area as Celestine Babayaro challenged.
By the half-hour mark Newcastle were struggling to escape from their own half, with one rare raid in the 33rd minute resulting in Stephen Carr firing wildly over from 20 yards after fine approach play from Babayaro and Bowyer.
Admittedly, by that stage, Bolton had not created many chances of their own as Newcastle were hardly being torn apart, but the home side were comfortably in control and did not look a team ready to relinquish their dominance.
Nine minutes from the break they deservedly broke the deadlock, with Nicky Hunt taking a lay-off from Stelios and delivering a piercing cross to the far post where Diouf powered home a header from four yards in off the right-hand post for his first of the season.
Within five minutes of the second half Souness was wearing the look of a worried man as Bolton doubled their lead with comparative ease.
Diouf chased down an overhit Hunt right-wing cross, and given time to pick his spot with his own ball, he found Speed at the near post for a flick to the far where Stelios tapped home from a yard.
There followed the inevitable cries from the Newcastle fans of 'We want Souness out, we want Souness out' - with a large section of Bolton supporters adding weight to the chants.
Bolton fans will be hoping that is not one of the last acts they see from Stelios as he continues to be linked with a move away, with Liverpool boss Rafael Benitez confirming his interest and now seemingly in a tussle with Manchester City for his services.
Wanderers could have added a third in the 70th minute, but Carr first headed away from underneath his own bar an inswinging Speed corner.
From the subsequent corner, Diouf was narrowly wide with a stabbed shot before United rallied in the closing stages as Shearer and Ameobi both went close - but by that stage it was too little too late.
Bolton Wanderers (4-4-2): Jaaskelainen; Hunt, Jaidi (Diagne-Faye, 23), Ben Haim, Pedersen; Nolan, Okocha, Speed, Giannakopoulos; Davies (Campo, 70), Diouf (Borgetti, 87). Substitutes not used: Walker (gk), Vaz Te.
Newcastle United (4-4-2): Given; Carr, Boumsong, Taylor, Babayaro; Bowyer (Milner, 67), Jenas, Faye (Clark, 60), Parker; Ameobi, Shearer. Substitutes not used: Elliott, Harper (gk), N'Zogbia.
Referee: R Styles (Hampshire).