After suffering consecutive 50-16 losses to the Cowboys and Wests Tigers in their last two outings, two late tries to rookie of the year contender Tui Lolohea saw the Warriors overcome a 10-point deficit to lead 22-20 in the last 10 minutes at ANZ Stadium.
But it wasn't to be; with England front-rower and Canterbury captain Graham barging his way over in the 77th minute, to see the finals-bound Bulldogs claim a fifth spot finish with a 26-22 victory.
The Belmore side will now prepare for an elimination final against the eighth-placed St George Illawarra Dragon at the same venue next Saturday.
Despite the cruel nature of the defeat the Warriors showed great character in the second-half after improving their play following a frustrating and error-ridden first 40 minutes.
The Warriors forwards showed a willingness to promote the football early on and a try to departing hooker Nathan Friend got them off to a good start, but mistakes quickly negated their attempts at expansive play.
Despite having numerous chances to extend their lead, bad ball control proved costly, with poor set finishes and no less than seven knock-ons inside the opposition red zone letting the hosts of the hook.
With Cronulla-bound five-eighth Chad Townsend back after missing the last two games with a groin injury, the Warriors directed much of their attack to the left, bar one clean line break from right-edge playmaker Mason Lino.
They continued to dominate territory but completed just eight of 19 sets, with two Bulldogs tries from Josh Morris and Curtis Rona leaving them trailing 8-6 at the break.
Fortune finally favoured the Warriors in the shadow of halftime, when Morris was ruled to have lost the ball as he attempted to ground the ball ingoal.
A repeat set at the start of the second-half gave young centre Solomone Kata the chance to reclaim the lead for the visitors, with his 12th try of the year seeing him overtake Manu Vatuvei to become the club's leading try scorer for the season.
But the Bulldogs lifted and struck back with two quick four-pointers to right wing Chase Stanley and impressive fill-in hooker Damien Cook, with front-rower Tim Browne converting both for what looked like the beginnings of an unassailable 20-10 lead.
But after almost two months of ill-fortune and uninspiring attacking play, the Warriors dug their heels in, and with much improved handling and discipline came back to stun Des Hasler's side.
A brilliant individual try to hot-stepping fullback Lolohea helped them shorten the margin to four, and five minutes later the 20-year-old dashed over for a second, before adding a third conversion to give his side a two-point lead.
They only had to hang on but the clinical Bulldogs smelled blood three minutes from time, with their skipper bounding through close to the ruck to deny the 13th-placed Warriors the much-needed yet ultimately elusive victory.
Bulldogs 26 (Josh Morris, Curtis Rona, Chase Stanley, Damien Cook, James Graham tries, Tim Browne 3 cons), Warriors 22 (Nathan Friend, Solomone Kata, Tui Lolohea 2 tries, Tui Lolohea 3 cons, pens).
