England scrum-half Harry Randall scored two tries as Bristol overcame Newcastle in pouring rain at Ashton Gate.
Injury has stalled Randall's career since his last England appearance in June but he showed glimpses of his best in a four-try win to move Bristol off the bottom of the Premiership table.
Tries from lock Chris Vui and flanker Fitz Harding secured the bonus point.
Flanker Gary Graham and hooker Jamie Blamire replied for Newcastle but they were left to rue missed opportunities.
The biggest of those came when Graham was held up over the line in the final minutes of the first half after he looked certain to score in the right corner.
It denied Newcastle a try that could have put them ahead at half-time but instead the boot of Jamie Williams extended Bristol's lead.
On a night when the rain made handling very difficult, Bristol managed the game better than their opponents for only a fourth win of the season and first home victory since September.
They produced the one flowing move of the match to score the opening try as fly-half AJ McGinty dummied to open a hole in midfield, passed outside to lock Joe Batley and his ball back inside sent Randall sliding over.
Graham almost immediately scored for Newcastle from close range but the visitors lost the kick-off and Vui eventually scored an identical try, also from a tap-and-go penalty.
Two minutes after the break Randall scored his second, this time from close range after Bristol exploited turnover ball to make ground down the left.
Newcastle hopes were lifted when a yellow card for Bristol winger Gabriel Ibitoye for a deliberate knock-on produced a penalty that Falcons kicked to the corner.
From the resultant line-out, Blamire dived into the right corner.
But it was Bristol pushing for a fourth try in the dying stages and after the hosts lost a line-out, Newcastle spilled possession near the own line and Harding pounced to swivel and dive over to seal all five points.
Bristol director of rugby Pat Lam told BBC Radio Bristol:
"We know that we're not a bottom-of-the-table team and we haven't performed at our best throughout the season.
"But since December we've really improved and we knew this was a big marker for us.
"There was a huge effort off the ball, a lot of work and a lot of fight and the boys got their rewards."
Newcastle head coach Dave Walder told BBC Radio Newcastle:
"I hoped we could dust the rust off early on but I don't think we ever did.
"I was disappointed we couldn't take our opportunities, particularly in the first half and I thought Bristol were clinical and played pretty well.
"We knocked a couple on close to the line, one held up over the line and in key moments it didn't fall our way."
Bristol: Heward, Naulago, Radradra, Williams, Ibitoye, MacGinty, Randall; Woolmore, Thacker, Lahiff, Batley, Vui, Luatua (c), Harding, Bradbury.
Replacements: Davies, Y. Thomas, Kloska, Holmes, Heenan, Uren, Ascherl, Lloyd.
Newcastle: Penny, Radwan, Moroni, Orlando, Carreras, Connon, Young (c); Brocklebank, Blamire, Davison, Peterson, De Chaves, Graham, Chick, Fearns.
Replacements: Fletcher, Mulipola, Palframan, Van der Walt, Lockwood, Stuart, Schoeman, Stevenson.
Referee: Karl Dickson