Pauleta has scored 47 goals in 83 international appearances
Pedro Pauleta, who almost scored after just 12 seconds, gave Portugal the lead on five minutes with a neat shot after Luis Figo's run and cross.
Cristiano Ronaldo hit the bar with a thumping header for Portugal, though Angola finished the half strongly.
The second half never quite lived up to the first half's promise though Pauleta and Maniche went close for Portugal.
Figo has spent most of international career patrolling the right flank for country, but at the age of 33 he is now deployed in a more central role, with Simao Sabrosa and Ronaldo doing the running for him.
Angola never quite got to grips with the freedom Portugal allowed Figo, who also provided a threat from set-pieces.
606 VIEW Angola just lacked that killer pass from midfield to provide any real threat
Xeno2
It was from a Figo corner that Ronaldo hit the bar with a powerful header on 35 minutes.
Just before the interval Ronaldo drew a fine save from Angola goalkeeper Joao Ricardo with a powerful shot.
On the hour Ronaldo was taken off by coach Luis Felipe Scolari, a decision that clearly angered the Manchester United forward.
Pauleta, who is Portugal's record goalscorer, might have given the European side the lead with the game barely 12 seconds old.
Sabrosa's pass released the Paris St Germain striker whose shot beat Joao Ricardo only to go the wrong side of the post.
Figo might be in the twilight of his career, but Portugal's captain still possesses an impressive burst of speed as he showed in creating the opening goal.
He sprinted past the leaden-footed Jamba before crossing for Pauleta, who sent a left-footed shot past Ricardo.
Making their World Cup debut, Angola must have feared the worst after that Pauleta goal, particularly as they had lost 6-0 and 5-1 in their two previous meetings with Portugal.
Figo was named as man of the match
But to their immense credit Angola refused to be overawed and went on the offensive.
Fabrice Akwa tried a couple of ambitious bicycle kicks, while Antonio Mendonca and Andre Mateus had long-range shots.
Three minutes before the interval another Angola shot, this time from Andre Macanga, drew a fine save from Portugal goalkeeper Ricardo.
The second half had a subdued opening, though Pauleta tried to reinvigorate Portugal with an ambitious curling shot and then a clever pass that set up a Tiago effort.
Scolari replaced Ronaldo with the more defensive Costinha as Portugal's coach attempted to close down the midfield, testament to the way Angola had rattled their European opponents.
While Portugal sought to protect their lead, Angola replaced Akwa with Pedro Mantorras, but the Benfica forward was unable to change the course of the game.
Substitute Maniche almost snatched a second Portugal goal late on with a rising drive.
Angola: Joao Ricardo, Jamba, Kali, Loco, Delgado, Figueiredo (Miloy 80), Macanga, Mateus, Mendonca, Ze Kalanga (Edson 70), Akwa (Mantorras 59).
Subs Not Used: Lama, Airosa, Lebo-Lebo, Rui Marques, Flavio, Love, Buengo, Mario, Marco.
Booked: Jamba, Loco, Macanga.
Portugal: Ricardo, Meira, Miguel, Nuno Valente, Ricardo Carvalho, Petit (Maniche 72), Tiago (Viana 82), Figo, Ronaldo (Costinha 59), Pauleta, Simao.
Subs Not Used: Quim, Paulo Ferreira, Caneira, Ricardo Costa, Boa Morte, Nuno Gomes, Paulo Santos, Postiga, Deco.
Booked: Ronaldo, Nuno Valente.
Goals: Pauleta 4.
Att: 45,000.
Ref: Jorge Larrionda (Uruguay).
Fifa man of the match: Luis Figo.
TRIVIA
Portugal's victory extended their unbeaten run in all matches to 15, the third longest current unbeaten streak in world football. It is already Portugal's longest ever undefeated sequence.
Petit, Luis Figo and Pauleta became the first Portuguese players ever to play at two World Cups. Nuno Gomes can join them if he plays during this World Cup. Portugal goalkeeper Ricardo won his 50th cap, five years after making his debut against the Republic of Ireland. He is the 18th Portuguese player to reach this milestone.
Angola played their first ever match at a World Cup but could not repeat Senegal's feat four years ago of beating a European team on their debut.
Angola przegrała w niedzielę drugi mecz grupy D z Portugalią 0-1. Spotkanie odbyło się w Kolonii

Portugalia spotyka się z Angolą po raz pierwszy na Mistrzostwach Świata. Wcześniej, drużyny te rozegrały dwa mecze towarzyskie, obydwa wysoko wygrane przez Portugalię: 6-0 (1989 r.) i 5-1 (2001 r.). 

Mecz, który zakończył się wynikiem 5-1 został przerwany po 68 minutach z powodu poważnych ubytków w zespole Angoli. Czterech z nich otrzymało czerwone kartki, a jeden doznał kontuzji. W sumie na boisku zostało sześcu zawodników tego kraju.