The Magpies were 3-0 up at half-time at the Reebok Stadium and forged ahead when French midfielder Charles N'Zogbia's free-kick from wide on the right evaded everybody in the box and curled inside Jussi Jaaskelainen's far post after 10 minutes.
They added a second 10 minutes later when James Milner crossed from the left and Obafemi Martins found space in the box and after controlling the ball he smashed in an overhead kick from close range.
Martins scored his second and Newcastle's third in the 27th minute when his low shot from the edge of the area took a wicked deflection off Abdoulaye Faye.
Bolton gave themselves a fighting chance as Kevin Nolan's clever pass released Nicolas Anelka and his angled finish made it 3-1 in the 50th minute, but Allardyce's men closed the game out.
Sven-Goran Eriksson claimed victory in his first competitive match as a club manager in England as Manchester City defeated West Ham at Upton Park.
Eriksson's first signing, Rolando Bianchi, put the Blues in front in the 18th minute as he tapped home from close range following a mazy run by Elano.
They made sure of the win in the 87th minute when Nedum Onuoha fought for possession on the right and cut the ball back to Geovanni, who slammed a shot past Robert Green.
Newly-promoted Derby County made a perfect start against Portsmouth but were pegged back for a 2-2 draw at Pride Park.
Stephen Bywater's long goal-kick was flicked on by Steve Howard and former Southampton midfielder Matt Oakley burst into the area and lashed in a shot after just four minutes.
However, Pompey equalised in the 27th minute when Benjani Mwaruwari's shot slid beneath the body of Bywater, who should have done better.
A Portsmouth new boy, Nigeria striker John Utaka, then gave Pompey the lead but it lasted only a minute after Gary Teale's cross from the right was met by a spectacular diving header by defender Andy Todd.
Blackburn overcame the loss of star striker Benni McCarthy to come from behind and beat Middlesbrough 2-1 at the Riverside.
A curling Stewart Downing free-kick gave Boro the lead at the interval and there was a massive blow for Rovers when McCarthy had to be carried off on a stretcher after suffering a head injury early in the second half. However, his replacement Roque Santa Cruz, newly signed from Bayern Munich, quickly scored the equaliser when he headed in David Bentley's cross from the right (63).
The winner came from England Under-21 striker Matt Derbyshire after curled in a shot from the edge of the box in the 79th minute.
Everton claimed an opening-day 2-1 win over Wigan at Goodison Park thanks to a 26th-minute header by Leon Osman and a 75th-minute goal by Victor Anichebe.
Antoine Sibierski pulled one back for the Latics from close range in the 80th minute but David Moyes' Toffees stuck together for the victory.