Hudson claimed the bonus-point try late on away to Zebre last Sunday and he repeated the trick as Matt O'Connor's men moved to the top of the RaboDirect PRO12.
Two tries in quick succession from Ashley Smith and Richie Rees had helped the Dragons move into a 16-10 lead approaching the hour mark.
However, the penalty count caught up with the Welsh region as they lost Nathan Buck and Jevon Groves to the sin-bin in each half and their new Argentinian prop Francisco Chaparro saw red for a dangerous 80th minute dump tackle on Isaac Boss.
Leinster notched all four of their tries while the visitors were down to 14 men.
They led 10-3 at half-time with man-of-the-match Jack McGrath returning from international duty to score his third try in ten league games this season.
Their scrum then turned the screw with two penalty tries while Groves was off the pitch, and Hudson was sent over in the right corner after Chaparro's dismissal.
The Dragons had to absorb the early pressure as Leinster turned down a kickable penalty, before Jason Tovey cleared the danger with a thumping kick downfield.
The penalties were beginning to stack up against the visitors - they leaked six in the opening 15 minutes - and a Rhys Thomas ruck offence allowed Ian Madigan to open the scoring.
Loose handling of the greasy ball and a messy scrum made for a listless first quarter, the game lulling along without either try-line being threatened.
However, a good spate of carrying - with captain Rob Sidoli and Nic Cudd making the hard yards - got the Dragons into scoring range and Tovey rewarded his pack with a well-struck drop goal.
Leinster struggled to build momentum as the turnovers and individual errors continued, but the sin-binning of Dragons prop Buck, who coughed up his fourth penalty when coming in at the side of a ruck, offered them a chink of light.
The men of Gwent also had to cope with Netani Talei's injury-enforced withdrawal and their resolute defence eventually gave way just before half-time.
Recent Six Nations debutant McGrath barged through a tackle from Sidoli and carried two more defenders over the try-line as Leinster ended the half with a seven-point lead.
But the doughty Dragons profited from two quick turnovers to produce a terrific turnaround early in the second period.
Just when Leinster looked set to score, centre Smith's vital tackle on Brendan Macken inspired a break downfield and although Fergus McFadden retrieved the situation, a further poach saw Matthew Pewtner hauled down short before he passed for Smith to finish in the right corner.
Tovey was unable to convert and he also sent the conversion of Rees' 48th-minute try wide, the scrum half dummying and scurrying through after the ball had gone loose from a midfield Leinster ruck.
It was helter-skelter stuff and Leinster were looking shaky as Tovey knocked over his first penalty of the night.
But Leinster's set piece strength got them back on track. Groves was yellow carded for collapsing a promising lineout maul and a subsequent set of close range scrums earned the Irish province their first penalty try.
The Dragons pack could not cope and leaked another penalty try in the 67th minute before Groves' return. Madigan converted both for a 24-16 advantage.
The visitors were not finished, Groves setting up a second penalty success for Tovey and a very competitive final 10 minutes.
They kept out Leinster's attempts to grind out a fourth try until a moment of madness from PRO12 debutant Chaparro, who lifted and drove Boss into the ground, saw them end the game shorthanded.
The home side piled on the pressure through their forwards, being held up just in front of the posts before Madigan's bouncing pass released Hudson for the bonus point score and the former added the conversion.
- Sports & Recreation
- Jevon Groves
- Francisco Chaparro
- Jason Tovey