A shocking penalty decision robbed Premiership newcomers Watford of the chance of a point against Everton.
Johnson opened his Everton account inside 15 minutes
The home side led 1-0 when Chris Powell was penalised for handling Tim Cahill's cross, even though the ball clearly struck the Watford player on the head.
Mikel Arteta calmly slotted home the resulting penalty to double Everton's lead after record signing Andy Johnson had marked his debut with a goal.
Damien Francis netted a deflected last-minute consolation for Watford.
The result was rough justice on the Hornets, who were the more positive team for much of the second half.
And their sense of injustice will be increased after the referee waved away their own appeals for a penalty after Ashley Young's cross appeared to hit Alan Stubbs on the arm.
Watford enjoyed good fortune, too, especially in the first half when Arteta hit the bar and Cahill headed against the post in a two-minute spell.
The visitors began well but were undone after 15 minutes as Johnson wasted little time in beginning to repay his £8.6m transfer fee.
The former Crystal Palace striker chested down James Beattie's pass and showed good strength before finding the net with a left-foot shot.
The Hornets did not crumble and caused the Everton defence some problems, although they were lucky not to fall further behind.
Arteta's free-kick left the crossbar shaking, then Cahill met Arteta's left-wing cross with a header which bounced off the inside of the post and rolled across goal.
Still the visitors came back, Francis unleashing a drive which Tim Howard grabbed at the second attempt and Gavin Mahon heading straight at the Toffees keeper.
Everton nearly doubled their lead on the hour mark when Johnson sent in a low cross that Beattie just failed to reach.
Still Watford came forward, with Hameur Bouazza's cross rebounding off the top of the bar and Francis sidefooting wide in a crowded penalty area.
Young also had a chance as the Everton defence opened up before him, but Howard was equal to it.
Watford's hopes were finally dashed by an appalling penalty decision.
Powell was sliding to block Cahill's cross, but the ball clearly rebounded off his forehead not his arm.
After Arteta had converted the spot-kick, Watford gained a deserved consolation when Francis found the net with a shot that went in off the post after hitting Stubbs.
Everton boss David Moyes
"Andy was always a threat and I hope that is the first of many goals for us.
"The fans were delighted when we signed him - he has a proven record in the Championship and the Premier League.
"His goal was excellent, along with all his work. Watford gave us trouble but we made it difficult for ourselves."
Watford boss Aidy Boothroyd
"It was human error and I have to wait half an hour before I can strangle the referee.
"But I don't want it to ruin a very pleasing performance. We will approach the Premiership in a positive light."
Everton: Howard, Neville, Yobo, Stubbs, Nuno Valente (Lescott 49), Davies (McFadden 73), Carsley, Cahill, Arteta, Johnson, Beattie (Anichebe 74).
Subs Not Used: Wright, Kilbane.
Booked: Beattie, Anichebe.
Goals: Johnson 15, Arteta 82 pen.
Watford: Foster, Doyley, Mariappa (DeMerit 45), Shittu, Powell, Chambers (Bouazza 45), Mahon, Francis, Young, King, Henderson (Priskin 79).
Subs Not Used: Lee, Spring.
Booked: Shittu, Francis.
Goals: Francis 90.
Ref: P Walton (Northamptonshire).