Bath dominated much of the territory in the first half but that failed to reap its reward on the scoreboard as three George Ford penalties was all they had to show for their efforts.
Instead, Sale were the side that displayed the incisiveness and tries from Vadim Cobilas and Will Addison, as well as seven points from the boot of Danny Cipriani, gave them a 17-9 lead at the interval.
To the visitors' credit, they continued to battle in the second period and deservedly levelled via Semesa Rokoduguni's touchdown and Ford's three-pointer.
But it was the Sharks who finished the stronger and Seymour and Easter went over from close range to keep them in contention for European Champions Cup qualification.
Mike Ford's men have struggled throughout the campaign and, despite a brief upturn in form following the Six Nations, last week's defeat to Saracens effectively ruled them out of the race for the top six.
No player has epitomised the West Country outfit's season more than Ford's son, George, who has failed to repeat his brilliance from 2014/15, where he thrived for both club and country.
The fly-half has been unable to continue that excellence this time around and the England international struggled early on against Sale.
Bath's stand-off put the opening kick-off into touch and then missed a penalty attempt after the forwards had forced a Sharks' infringement at a maul.
It allowed the hosts to withstand the initial pressure and, with their first chance, the Manchester side scored the first points of the afternoon via Cobilas.
Mike Haley was the instigator, dancing his way through the heart of the visiting rearguard, before the Moldovan prop picked up and drove across the whitewash from close range.
Ford then showed impressive patience and control to guide the team around the field. That led to a three-point opportunity which the pivot converted, but they struggled to build on that as Steve Diamond's men remained a threat with ball in hand.
Cipriani, as has often been the case in the previous two years, was dictating proceedings superbly and, after he sent Sam Tuitupou into space, the centre linked with midfield partner Sam James.
That gave James the chance to ship the ball out to Addison and the winger did the rest, stepping inside one defender and holding off the attentions of Ollie Devoto to touch down.
As the opening period neared its conclusion, Bath thought they had reduced the arrears following a Rokoduguni interception, but it was called back for a deliberate knock-on by Sale-bound Rob Webber and the hosts' fly-half extended the Sharks' buffer.
Ford kept the visitors in contention with a third effort off the tee on the stroke of half-time, but they required far more incision after the break.
That clinical edge duly materialised immediately after the interval as excellent work from Devoto and Ford sent Rokoduguni over in the corner.
It was a response their pressure deserved and minutes later Bath were level via the boot of their pivot, who slotted a penalty following yet another Sale infringement.
With the Manchester outfit on the back foot, they attempted to hit back and earned a shot at goal but, for the first time in the match, Cipriani was off target.
Bath's stand-off followed suit soon after from a much easier angle as the teams went into the final stages locked at 17-17.
However, it was the Sharks that lifted the intensity and the pressure eventually resulted in a yellow card for Dominic Day. Down to 14 men, Ford's men failed to cope with the hosts' driving maul and Seymour crashed over for the decisive score
Cipriani's conversion attempt was controversially ruled not to have gone over but it didn't matter as Sale secured the win via Easter's try to condemn Bath to another defeat.