A deflected first-half strike from academy graduate Anthony Gordon decided the match, helping Lampard's side recover from a destressing midweek loss to Burnley.
The 3-2 defeat at Turf Moor last time out sucked Everton straight into the midst of a relegation battle, but they've since responded to move four points clear of the bottom three with a game more played.
Lampard's record at Everton still doesn't make great reading since his January arrival with three wins and seven defeats in 10 league games, but home form has been a comfort.
The Chelsea legend now has three wins from five league games at Goodison Park, and he was keen to acknowledge the crowd's role in an important home victory.
When asked by talkSPORT what the result meant, Lampard said: "Three points, we need more of that so won't get carried away but we've been good here at Goodison.
"My time here we've got five wins in the seven games [in all competitions], we don't concede, we fight, the crowd get with us and we create something a bit special like today.
"We just need to go again with that, the next game's at home and we've not yet strung wins together in the league, so I'm really happy with how the whole stadium was, it was another special one but we've got more to do, I'm not jumping up and down because there is a lot more to do."
Lampard felt his side were judged harshly after a chaotic defeat to Burnley, where they found themselves 2-1 up before being out-gunned.
But a visibly delighted Everton boss was over-the-moon with his side's recovery and ability to shrug off what could have been a catastrophic loss.
"We didn't deserve to lose against Burnley," he explained. "The biggest thing today was the character of picking ourselves up.
"Thursday morning it feels horrible, Friday morning not so bad, Saturday morning you go again against Man United, so that's why I'm proud of the players and the fans.
"We were all very upbeat, fighting until the last minute, and at the minute that's the difference a little bit.
"We've got to deal with the away stuff but at the minute the football basics are much more important than the pretty patterns, it's the fight and the tackles and the running that are going to keep us up.
"We're not soft. As much as we bemoan the stakes late in the game at Burnley, when you get in that position here with a high level team such as Manchester United, they've only got to get the ball one time through your midfield and you've got people like [Cristiano] Ronaldo and [Bruno] Fernandes running at your back four, you have to manage the game.
"As I say, we're in a moment now where that side of the game is more important than the beautiful side so well managed by the lads."
United outshot Everton 12-7 during the match, with four efforts to three on target, and Lampard was delighted with Jordan Pickford's ability to snub out any potential threats.
Asked about Pickford's impact, Lampard said: "Big, big, he's England's number one.
"He's a pleasure to work with Jordan, I have to say, and the scrutiny that comes with that role as England's number one is big.
"The saves he makes, I don't think they were amazing chances the first two but they were really good saves and the Ronaldo one, with our luck recently you expect that to bulge the net.
"You need to rely on your keeper, top goalkeepers are a big deal, they win you points and save you points and Jordan did it today."