The diminutive fullback scored another wonder try and set up three more as Des Hasler's team were made to work hard for their two points by a depleted but much-improved Eels side.
The lowly Eels, who were without the injured Jarryd Hayne and Matt Keating and the suspended Ben Smith, lost Fuifui Moimoi in the opening hit-up when he was caught across the jaw by the swinging arm of Sam Kasiano.
Moimoi was slipping as he went down, but giant Kasiano was placed on report for the incident which saw the veteran prop helped off the field.
The early signs looked ominous for the Eels, who shipped 34 points in the first half against Manly last week, with Josh Morris scoring a fifth-minute try.
Barba then added another entry to his highlights video when he fielded a Chris Sandow grubber-kick in front of his own posts, shrugged off three tackles and raced the length of the field to score.
But the visitors responded well and cut the deficit when Ken Sio hauled in a Luke Kelly kick for his ninth try of the season.
It was the start of a sustained spell of pressure, but they were unable to breach the Bulldogs defensive line, and were punished for their profligacy when Morris went over again on the stroke of halftime.
Despite that blow, Parramatta came out firing after the interval and scored a superb try through Ryan Morgan after good work from Sandow and Kelly, with Luke Burt's kick closing the gap to 16-12.
However, like so often this season, the Eels shot themselves in the foot with some silly errors to undo all of their good work.
After defending two sets on their own line, Nathan Hindmarsh offloaded the ball forward on the first tackle, and from the resulting scrum Barba fed winger Jonathan Wright to score.
And in the 65th minute Sandow threw a pass straight into the arms of Inu to gift the Bulldogs possession and Josh Reynolds added the finishing touches as the home side marched down the field to score.
And to add insult to injury, Wright, one of three former Eels in the Bulldogs side, scored his second try, four minutes from time, with Inu kicking his fourth conversion of the game.
Meanwhile, Brisbane coach Anthony Griffin prepared his players for an 80-minute grind all week and that's exactly how their NRL clash with the Warriors unfolded at Suncorp Stadium on Friday night.
In the end, Brisbane emerged from the battle in wet and slippery conditions with a narrow 10-8 win in front of a crowd of 32,148.
The Warriors almost pulled off a stunning last play in the dying seconds before fullback Josh Hoffman dragged down giant Warriors winger Manu Vatuvei who flung the ball back infield to James Maloney.
With the siren blasting in the background, Maloney put a crossfield kick into the left corner which Brisbane winger Gerard Beale only just managed to bat over the dead ball line as a miracle try loomed large.
Brisbane snuck home on the boot of lock Corey Parker, whose 55th-minute penalty from 20 metres out broke an 8-8 halftime deadlock.
His goal was the only points of a dour second half defensive arm wrestle in a game which could have gone either way right until fulltime.
Brisbane bashed their way to a win but at a cost.
Young winger Dale Copley was forced from the game midway through the first half with a shin injury while skipper Sam Thaiday copped Vatuvei's left knee flush on the jaw that forced him off in the second half.
Initial fears were Thaiday may have broken his jaw but the Origin star, who was not knocked out but heavily dazed, showed plenty of courage to return to the action and produced two tackles late in the half as the Warriors repeatedly threatened the Broncos line.
As expected, defence dominated with Parker backing his outstanding Origin form with 55 tackles while busy hooker Andrew McCullough (47) and starting prop Josh McGuire (44) also produced whole-hearted efforts.
It was a similar story for the Warriors with hooker Nathan Friend topping the tackle count with 47 closely followed by skipper Simon Mannering (45).
Unfortunately for Maloney it wasn't his night with the boot, missing all three shots for goal.