John Murphy's early try put the Tigers on their way
Leicester: (20) 41
Tries: J Murphy, Penalty, Buckland, Jennings, Humphreys
Cons: Burke 3, Humphreys 2
Pens: Burke 2
Dragons: (10) 17
Tries: Williams, Morgan
Cons: Warlow, Sweeney
Leicester overcame spirited resistance from the Dragons to start their EDF Energy Cup campaign with a bonus-point victory at Welford Road.
The Tigers led 20-10 at half-time via two Paul Burke penalties, a Johnny Murphy score and a penalty try, Scott Williams crossing for the Dragons.
Further tries from James Buckland and Shane Jennings effectively put the outcome beyond doubt.
Kevin Morgan scored for the Dragons but Ian Humphreys had the last word.
The visitors had threatened to get back into it when they sent on Welsh internationals Gareth Cooper, Ceri Sweeney, Colin Charvis and Michael Owen on the hour, and were rewarded with Morgan's try after a flowing move.
But replacement fly-half Humphreys waltzed through a tiring defence in the final minute, converting his own try to put the seal on the Tigers' victory.
They led 13-0 after the opening quarter when lock James Hamilton's charge and pass sent Murphy over after a pair of early Burke penalties .
But Craig Warlow kicked a penalty and Williams intercepted a Humphreys pass to race over, Warlow's conversion making it 13-10.
When Dragons back-row James Harris was sin-binned for killing the ball, Leicester's pressure told when they were awarded a penalty try after a five-metre scrum.
A stunning 60m break from Dan Hipkiss was halted by Morgan but Leon Lloyd put Buckland over in the corner, and when Jennings charged round the blind side of a line-out to score, the game was effectively up.
Leicester wing Tom Varndell, on loan at Bedford, scored the opening try on his debut to help the Blues to a 22-10 National League One win over Exeter.
"I think he's a very good player but I'm not going to make it easy for him," said Leicester head coach Pat Howard.
"Tom at his best is an outstanding finisher and I'm trying to get him at his best.
"He's still a young bloke with a reasonable amount of pressure on him and he is not playing at his best.
"If he performs to the best of his ability he will be in the team."
Leicester head coach Pat Howard
"We made a fair few line breaks and we were dangerous a reasonable amount of the time.
"But our finishing has been a consistent issue this season and that may have been a bigger problem against the better sides."
Dragons head coach Paul Turner
"This is a hard place to come to and there were too many unforced errors from senior players.
"At half time we thought it was anybody's game but the game goes away from you very quickly at places like this.
"The breakdown was a war zone and some of the decisions went against us in that area. At 27-10 we had a couple of sniffs and that could have made a difference."
Leicester: J Murphy, Lloyd, Hipkiss, Smith, A Tuilagi, Burke, Bemand; Ayerza, Buckland, Castrogiovanni, Hamilton, Cullen (capt), Moody, Jennings, Crane.
Replacements: Chuter, White, L Deacon, B Deacon, F Murphy, Humphreys, Gibson.
Dragons: Morgan (capt), Chapman, N. Brew, Williams, A. Brew, Warlow, Baber, Maddocks, Daly, Harrison, Griffiths, Charteris, Hall, Harris, Fitisemanu.
Replacements: Crawford, Thomas, Owen, Charvis, Cooper, Sweeney, Fussell.
Referee: W Barnes (RFU)