Dobson converted Scott Murrell's 61st-minute try.
But Thomas Bosc's 77th-minute drop-goal sealed the points for the Dragons and Baile completed his superb personal display in the penultimate minute.
On Friday night, Stefan Ratchford touched down twice and was inspirational throughout as struggling Salford beat leader St Helens 20-10.
The rangy halfback, 21 later this month, claimed his two tries in the first 10 minutes and fullback John Wilshere converted both to put the Reds 12-0 up.
Remarkably, a third score arrived in the 16th minute when Ratchford orchestrated a fine move which culminated in centre Darrell Goulding crossing in the left corner.
Salford deservedly led 16-0 at the break and, though Saints responded in the second half with a try through young replacement Andrew Dixon, there was no comeback.
The Reds lost stand-off Jeremy Smith to the sinbin in the 53rd minute but their workrate and desire harvested a fourth try five minutes later when wing Mark Henry touched down to send a raucous home crowd into raptures.
Francis Meli claimed a late consolation for the visitors in the 79th minute but the result ended Saints' record-breaking run of 16 straight away wins on a night when nothing worked for Mick Potter's side.
And their misery was compounded after it was revealed scrum-half Sean Long suffered a suspected broken jaw.
In Friday night's other game, Wigan ran in eight tries as they brushed aside a feeble Harlequins 40-12.
The Londoners had already conceded early tries to Pat Richards, Mark Riddell and Karl Pryce when David Howell was sent off for a head-high tackle on Sam Tomkins.
Wigan made their numerical advantage count and ran out convincing winners at the JJB Stadium with further tries from George Carmont, Amos Roberts, Joel Tomkins and two from Thomas Leuluai.
Luke Gale and Matthew Gafa crossed for Quins.