The Brazilian midfielder headed home in the eighth minute at the Europa-Park Stadion as he got on the end of Jarrod Bowen's inviting delivery from the right.
It was a cross that showed exactly why Gareth Southgate has recalled the winger back into his England squad for the upcoming clashes against Australia and Italy.
The ex-Hull man put in a lofted cross from the right flank towards the penalty spot, with Paqueta towering above his marker to head beyond the outstretched arms of Noah Atubolu.
Speaking on talkSPORT 2 commentary, Alex Crook said: "Jarrod Bowen, once again, played a massive part.
"As the ball was played into his feet down the right-hand side by [Vladimir] Coufal, it's a delicious ball into the area.
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"And Paqueta with the header makes it Freiburg 0-1 West Ham."
Ex-Hammers left-back Minto added: "I tell you what, one, that was a delicious ball, right foot, he's out wide, he didn't even go past the defender.
"But he got the half-a-yard, so he's able to put them in, but what a header from Lucas Paqueta.
"It reminded me of Mark Hateley back in the day and an-Alan Shearer type header.
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"He leaps above two defenders, and gives it such power, and also precision, giving the 'keeper no chance whatsoever.
"And how talented he is with the ball on the ground, to see him do that in the air, wow, amazing. It's just a brilliant start for the Hammers."
Paqueta then thought he had scored another after rifling the ball into the roof of the net from close range, but the former Lyon maestro was adjudged to be offside.
Having missed a number of chances in the opening period, Freiburg equalised through Roland Sallai in the 49th minute.
The German side then threatened to go in front, but Nayef Aguerd got on the end of James Ward-Prowse's corner to head in in the 66th minute.
David Moyes' side held on for the crucial three points to remain top of Group A.
And after avoiding victory, West Ham have become the first English side to go 17 successive games unbeaten in Europe.