|Bath (12) 21|
|Tries: Rokoduguni 2 Con: Homer Pens: Homer 3|
|Newcastle (7) 19|
|Try: Vickers Con: Delany Pens: Delany 4|
Bath secured a tense victory over Newcastle to leave the Falcons without a Premiership away win in 18 months.
Newcastle hooker Rob Vickers bundled over to put the visitors ahead before Semesa Rokoduguni showed fine footwork to set himself up for Bath's first try.
The wing then sprinted in for a second to give Bath a 12-7 half-time lead.
Mike Delany slotted four penalties to put Falcons in front with two Bath men in the sin bin, but Tom Homer's penalty gave the hosts victory.
Falcons earned a losing bonus-point but the defeat means the Kingston Park outfit are now without an away victory in the league since they beat London Welsh in October 2014 - a run of 16 losses and a draw.
Dean Richards' side were the better team for much of the first half but could only put seven points on the board through Vickers' converted try.
They were made to pay as Rokoduguni somehow controlled Ollie Devoto's wayward cross-field kick with his boot and crossed the whitewash.
Francois Louw's fine break then put Rokoduguni in again, but Louw turned from hero to villain in the second half when he was sin-binned along with Henry Thomas as Newcastle took a brief lead through Delany's boot.
However, Falcons hooker Scott Lawson soon received a yellow card himself for tackling without arms and Homer slotted through the resulting penalty from the tee.
Delany tried desperately to land a drop goal in the final few minutes, but last year's beaten Premiership finalists held on for just their sixth win of the season.
Bath first-team coach Neal Hatley:
"The cavalry is appearing over the hill. All we talked about this week was getting a win and getting those players back next week.
"Going into next week at Gloucester on the back of a defeat would have been a real downer.
"Semesa Rokoduguni has been outstanding all season in a side that has been nowhere near as fluent as we'd like to be or as we were last year. He either goes round you or over you - and he's unbelievable in the air. He's been a real constant for us and long may it continue. He brings a lot of X-factor."
Newcastle Falcons director of rugby Dean Richards:
"We probably left 16 to 18 points out there on the field. It's frustrating for the players. They are sitting in the dressing room kicking themselves because they're thinking they probably did enough to win today.
"They know where they went wrong and they'll be out there on the training pitch next week trying to put it right.
"We'll get there. It's coming and we haven't had a selection issue before but we starting to get one now because people are putting their hands up and saying: 'Pick me'."
Bath: Homer; Rokoduguni, Banahan, Clark, Williams; Devoto, Cook; Lahiff, Webber, Wilson, Hooper (capt), Day, Garvey, Louw, Houston
Replacements: Dunn, Catt, Thomas, Ewels, Mercer, Evans, W Homer, H Agulla.
Newcastle: Hammersley; Venditti, Harris, Socino, Watson; Delany, Takulua; Vickers, McGuigan, Vea, Botha, Green, Wilson, Welch (capt), Latu
Replacements: Lawson, Rogers, Hatakeyama, Robinson, Hogg, Young, Willis, B Agulla.