Olly Barkley had missed penalty opportunities which allowed the hosts to gain the initial advantage, before Cory Harris was sent to the sin bin just before the interval. The visitors then scored four tries - through Matt Stevens, Martyn Wood, Isaac Feaunati and James Scaysbrook - to claim a bonus point.
Bath started brightly, with the hosts barely touching the ball before Barkley opened the scoring with the simplest of penalties for offside. However, the England international missed his next three kicks - all from awkward angles on the left.
The Australian veteran Matt Burke, in contrast, coolly kicked the hosts level from a simple position after eight minutes. Burke relieved Dave Walder of kicking duties, but the England hopeful executed a 25th-minute drop goal.
Burke extended the lead with another penalty, and the first try of the afternoon was also provided by Burke after he received a pass from Walder in the 38th minute. Burke tricked two opponents with his dummy to score.
Stevens reduced arrears in first-half injury time when he stole in on the blind-side, before Harris saw yellow for an infringement in a maul.
Bath were within a point in the 48th minute through Wood after an advantage from the referee Ashley Rowden. Wood's pass hit Andy Perry in an offside position, and while players appealed the Bath man scored. Barkley converted.
The visitors were ahead in the 58th minute when Feaunati was bundled over after a drive, with Barkley converting. The bonus point was sealed when Scaysbrook crossed.
Newcastle: Try Burke; Conversion Burke; Penalties Burke 2; Drop goal Walder. Bath: Tries Stevens, Wood, Feaunati, Scaysbrook; Conversions Barkley 2; Penalty Barkley.
Newcastle: M Burke; A Elliott, J Noon, M Mayerhofler, M Tait; D Walder, H Charlton; M Ward, A Long, R Morris, A Perry, G Parling, O Finegan, C Harris, C Charvis (capt). Replacements: D Wilson, M Thompson, T Paoletti, M McCarthy, B Woods, J Grindal, T Flood.
Bath: M Perry; D Bory, T Cheeseman, O Barkley, A Higgins; A Dunne, M Wood; D Barnes, D Mears, M Stevens, S Borthwick, D Grewcock, A Beattie, J Scaysbrook, I Feaunati. Replacements: P Dixon, D Bell, G Delve, J Hudson, N Walshe, S Finau, S Davis.
Referee: A Rowden (Berkshire).