Number eight Gary Graham scored twice and wing Ben Stevenson provided the other Newcastle try. Victory was no less than they deserved for a confident, committed team effort.
Fly-half Brett Connon missed a straightforward chance to put Newcastle ahead early on and it was Bath who scored first, with a try by Cokanasiga after nine minutes.
The England wing was first involved out on the left touchline after a break by Rhys Priestland and popped up again on Cameron Redpath’s shoulder to take a deft offload. Priestland converted for a 7-0 lead.
The home side could have been further ahead shortly afterwards. But Ben Spencer’s touchdown was ruled out by the TMO because Redpath had knocked on rather than been stripped of the ball when tackled just short of the line by Luther Burrell and Tom Penny.
Bath were showing plenty of ambition but their attempts to gain control of the game were stymied by penalties conceded at the breakdown and turnovers.
Graham grabbed a well-earned try for the visitors after 22 minutes, fed from a quickly taken line-out by Michael Young. Connon could not convert.
The fly-half was also wide with a long-range penalty on the half-hour but did convert a second try by Graham just before the break to give Newcastle a 12-7 half-time lead.
Bath found their rhythm after the break to fashion a classy try for Matavesi against his former club but it was unconverted and the visitors hit back almost immediately when Stevenson dived in at the corner. Connon’s kick opened up a seven-point margin.
There was no letting up though and the Bath defence had to work overtime to keep out a constant barrage of attacks in a frantic third quarter as veteran Toby Flood orchestrated affairs in the Newcastle midfield.
England lock Charlie Ewels came off the Bath bench to add his bulk and leadership qualities but came under scrutiny for a robust front-on tackle on Adam Radran which earned a yellow card. Connon was just wide with the penalty.
Priestland missed a long-range penalty as Bath struggled to get out of their half and they needed the sort of encouragement that replacement Semesa Rokoduguni provided with a crunching tackle on Penny.
But it was Newcastle who finished well in control, looking for the try bonus point.
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