Atalanta forward Lookman, the former England Under-21 international, had scored both goals in Nigeria's defeat of Cameroon in the last 16 and he made it three in two games as the Super Eagles claimed their third 1-0 victory of the tournament.
The goal came four minutes before half-time at the Felix Houphouet Boigny Stadium, with Moses Simon collecting a pass on the left, accelerating away from Kialonda Gaspar and driving into the area before cutting the ball back for Lookman to finish.
That was enough for Nigeria to win through to their 15th Cup of Nations semi-final, which is more appearances than any other country.
Reigning African footballer of the year Victor Osimhen found the net with a quarter of an hour remaining but his effort was disallowed for offside and the Napoli striker is therefore still without a goal since Nigeria's opening 1-1 draw with Equatorial Guinea.
Meanwhile Angola had one golden chance to equalise just before the hour mark, when substitute Zini was sent through on goal but his shot came back off the post.
Nigeria have now kept four consecutive clean sheets, validating coach Jose Peseiro's approach which has been based around making sure they do not concede goals first and foremost.
"They are a good team, but once again we didn't concede. Once again we scored once," Peseiro said.
"I would have liked to score more. With better finishing we could have scored another one or two goals, but I am happy. My players deserved it."
Nigeria advance to a last-four tie next Wednesday against Cape Verde or South Africa in the central Ivorian city of Bouake -- those sides meet in the quarter-finals on Saturday.
Angola, meanwhile, go home but this AFCON will be remembered as a success for the Black Antelopes, after they won a knockout tie at the tournament for the first time ever.
"We said among ourselves that if we got to the quarter-finals we would then try to win the tournament. Any team that comes this far has that ambition," said Angola's Portuguese coach Pedro Goncalves.
"We like to dream, but you also need to be realistic. The reality is that we were up against a very powerful side with players who play at the very highest level."
- Masuaku stunner -
Friday's second match saw DR Congo see off Guinea 3-1 across Abidjan at the Ebimpe Olympic Stadium.
Guinea had reached the last eight after winning a Cup of Nations knockout tie for the first time, and they went in front midway through the first half.
Mohamed Bayo was pushed over in the box and converted the resulting penalty for his third goal of the competition.
However, Leopards captain Chancel Mbemba produced a fine finish to equalise before the half-hour mark, and the Congolese took the lead with a penalty of their own in the 65th minute.
Silas Katompa Mvumpa was tripped in the box by Julian Jeanvier, and Yoane Wissa of Brentford made no mistake from the spot.
DR Congo then clinched their place in a first semi-final since 2015 thanks to a stunning late free-kick by Besiktas full-back Arthur Masuaku from way out on the left flank.
They had qualified for the knockout phase despite drawing all three matches, and then overcame Egypt on penalties in the last 16.
"We are extremely happy because we had drawn all our games up to now and we picked a good moment to get a win," said their French coach Sebastien Desabre.
DR Congo now stay in Abidjan for a semi-final against either Mali or hosts Ivory Coast, who meet in the last eight on Saturday.
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