Rotherham battled from start to finish in the second play-off semi-final at Abbeydale in front of more than 3,000 but their brave efforts to reach the Championship final ended in disappointment.
Bristol now face Worcester in the final, but were given a genuine fright as Rotherham at one stage cut their overall lead to only two points.
Bristol finished the stronger team when they scored tries on 60 and 73 minutes, but before then three penalties by fly half Tom Barrett on 16,28 and 38 minutes had put the Titans 9-3 in front.
This was improved upon in thrilling style early in the second half when winger Jamie Broadley collected a loose ball and dashed 45 metres to the Bristol line to touch down for an outstanding try. And with Barrett converting, Rotherham led 16-6,and importantly, they were behind by just two points on aggregate.
Bristol looked stressed, but with Rotherham continuing to give away penalties and losing some line-out ball, the favourites gradually began to assert their authority.
Rotherham’s attitude and spirit should make their supporters proud. They were never outclassed, but could not cope with the strength of the Bristol replacements.
On the hour, Bristol scored a cracking try by flanker Marco Mama and added a second 15 minutes later as centre Jack Tovey completed a move that ruined the Rotherham defence.
With the conversion, that took Bristol in front by 21-16 - a total lead of 17 points.
Bristol were now well on top and deep into injury time, the former Wales and British Lions star, Gavin Henson, struck his fourth penalty.
The defeat brings an end to Rotherham’s Championship season and of Lee Blackett’s two successful years as their coach. He’ is moving to Premiership club Wasps, but before then he will be on the interview panel next Friday to select his successor.
“ I’m really proud of the efforts we put in over two legs. We finish the season as the top club in Yorkshire. The attitude was outstanding.
“The difference in both the games was the strength of the Bristol bench. But in both matches we were the better side for the first 60 minutes.
“ My successor is left with a great bunch of players and I am sure Rotherham will continue to be a threat in the Championship.”
There were solid and inspiring performances from forwards Alex Rieder and Ali Birch, among others, and in the backs Lloyd Hayes, Sean Scanlon and Broadley.
Rotherham also defended effectively and managed to prevent Bristol from smashing their line until 60 minutes.
Rotherham Titans: Scanlon,Broadley, Hayes,J.Davies, Keating, Barrett,A.Davies, Hislop, Cruse, Tampin, Maddison,Robinson, Rieder, Birch, Morris. Replacements: Preece, Williams, Thiede,Thomas, Argyle, White, Roberts.
Penalties: Barrett: 3.
Referee: Dean Richards.