The club-record signing from Everton had a goal chalked off before finally breaking his duck in his sixth appearance since his deadline-day switch to the King Power Stadium with a well-placed header nine minutes before half-time.
Beckford's strike partner David Nugent opened the scoring after 19 minutes.
Watford were disappointing and rarely threatened, with Sean Dyche's side only looking dangerous on a handful of occasions from set-pieces.
Jonathan Hogg came closest for the Hertfordshire club when his thunderous volley from the edge of the area was pushed over the crossbar by Kasper Schmeichel with four minutes remaining.
A fourth straight home win lifted Leicester to within a point of a top-six spot, while the same margin is all that separates Watford from the relegation zone after a third successive defeat.
Foxes boss Sven-Goran Eriksson made four changes following the defeat to Birmingham on Sunday. One was enforced with Matt Mills beginning a three-match suspension for the red card he received at St Andrews. As expected, Sean St Ledger replaced the City captain at the heart of the defence.
Richie Wellens returned and took the armband and he was partnered by Michael Johnson in midfield as Neil Danns and Gelson Fernandes dropped out of the starting line-up. Beckford came in for Darius Vassell.
Like Leicester, Watford were beaten 2-0 at the weekend and Dyche made three changes.
David Mirfin replaced Martin Taylor after the big defender suffered a collarbone injury against Crystal Palace, while Troy Deeney and Chris Iwelumo were recalled at the expense of Craig Forsyth and Marvin Sordell.
Leicester thought they had been rewarded for their bright start in the ninth-minute when Beckford's volley looped over goalkeeper Scott Loach, but the ball was adjudged to have gone over the left byline before Sol Bamba had dug out a cross.
Beckford was almost presented with another opportunity to score five minutes later when Loach came sliding out to collect Paul Konchesky's through ball.
The one-time England squad member spilled the ball but Beckford was at too acute an angle to fully capitalise.
Konchesky was involved again when Leicester opened the scoring.
A delightful first touch from Nugent when collecting Konchesky's pass took him past two defenders and into the Watford penalty area, where he sent a left-foot shot across Loach and into the far bottom corner for his fourth goal of the season.
Only a fingertip save from Loach on the half-hour denied Nugent a similar goal - this time from the right-hand side.
Leicester deservedly extended their lead in the 36th minute when Yuki Abe's right-wing cross was glanced home by the head of Beckford.
Adrian Mariappa came close to halving the deficit early in the second half. His header from 15 yards looped over Schmeichel but dropped on the roof of the net.
Eriksson's side were less of a threat after the break and did not really threaten again until the 78th minute.
Substitute Vassell, on as a replacement for Beckford, had a curling effort from inside the area deflected just wide. Bamba headed over from the resulting corner.
Andy King then had Loach scrambling across his goal with a curler from 18 yards, but again the ball went narrowly wide.
Hogg worked Schmeichel for the first time in the 86th minute but the Leicester goalkeeper showed good agility to keep him out.
Any reproduction, publication or redistribution of this material without the written agreement of 365 Media Group is strictly forbidden.