Kallum Watkins put the hosts ahead and they extended their lead when Danny McGuire's kick bounced off the crossbar and fell for Matt Parcell to score.
Tom Gilmore reduced Widnes' deficit but Joel Moon crossed for a second time and Tom Briscoe sent them 30-6 ahead.
Gilmore and Chris Houston touched down in the second half but Watkins and Parcell scored again to seal the win.
The victory means Leeds are level on points with league leaders Castleford Tigers, who were beaten 26-22 against St Helens on Monday, but have played one game more.
Corey Thompson ran in Widnes' fourth try after the hour mark to make it 30-22 and they could have been within a converted try of levelling the scores, but Gilmore missed the extras.
Despite their spirited second-half comeback, the Vikings could not close the gap and remain rooted to the foot of Super League, having won just once in their opening 10 games.
Widnes also lost Tom Armstrong (knee), Danny Craven (finger) and Lloyd White (hamstring) to injury in the defeat.
It was the first time Leeds had won against Widnes since beating them 38-6 in February 2015, with Denis Betts' side winning their three meetings after that defeat.
Leeds Rhinos head coach Brian McDermott:
"There were a couple of things involved in the second half, not least Widnes' desire to get back into the game. But we were running at 40% in the second half and the last thing we needed to do was give them an invite back into the game.
"Credit to Widnes - they made it a contest but had we done things differently they never would have been able to make it a contest.
"We found ourselves in a situation where we were fighting for the game and credit to our players - they showed some maturity and when they got the chance they got over to score a try.
"I won't get on the players' backs about the second half - it made it interesting and entertaining - but the most pleasing thing is that we were very good and very clinical in the first half."
Widnes Vikings coach Denis Betts:
"At half-time we spoke about treating it like someone taking something from us in the street and then chasing after them and trying to get as much as we can back.
"We got ambushed at the start and we intended to start quickly ourselves. But we were only competing at 60% and got behind in the penalty count and then we just got caught in a whirlwind of incomplete sets and injuries.
"We're down on troops and it's a tough time at the moment. We'd like to take credit for the second half - they ran out of steam a little bit too."
Leeds: Handley, Briscoe, Watkins, Ward, Hall, McGuire, Moon, Galloway, Parcell, Cuthbertson, Jones-Buchanan, Delaney, Mullally.
Replacements: Burrow, Walters, Garbutt, Baldwinson.
Widnes: Thompson, Marsh, Armstrong, Runciman, Ah Van, Craven, Gilmore, Buchanan, White, Chapelhow, Houston, Dean, Farnworth.
Replacements: Dudson, Walsh, Burke, Johnstone.
Attendance: 15,408.
Referee: Scott Mikalauskas (RFL).

Surrey Fire Service said it started at about 14:00 BST at a nearby nature reserve and spread across 25 acres.
More than 40 firefighters, six engines and two water tankers were used to deal with the blaze.
Alan Clark, from Surrey Fire and Rescue Service, said "the lack of rain and tinder box dry conditions provided the perfect recipe for wildfires".
He added: "Once they start they can spread quickly, making wildfires notoriously difficult to control."
The Wentworth golf estate regularly hosts major golf tournaments including the PGA championship and World Match Play Championships.
Leeds kept up the pressure at the top of the Super League as they survived a second-half comeback to beat Widnes.
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A wildfire which spread onto the Wentworth golf estate has been tackled by firefighters.