QPR contributed an own goal, lost new signing Kieron Dyer to a foot injury and had defender Clint Hill sent off in injury time.
Newly promoted Norwich drew 1-1 at Wigan, Aston Villa drew 0-0 at Fulham and Wolverhampton Wanderers won 2-1 at Blackburn.
Liverpool started new signings Jordan Henderson, Stewart Downing, Charlie Adam and Jose Enrique against Sunderland and led at Anfield through Luis Suarez’s 12th-minute goal.
But Suarez also missed a penalty and the Reds failed to capitalize on their domination. Sebastian Larsson equalized in the 57th to clinch a 1-1 draw.
Manchester United opens its title defense at West Bromwich Albion on Sunday, when Chelsea is at Stoke.
QPR lost Dyer, the former England winger signed on a free transfer from West Ham, early on when he fell awkwardly and Bolton took the lead moments before halftime when central defender Gary Cahill scored with a curling shot.
Debut-making defender Danny Gabbidon scored an own-goal in the 67th, Ivan Klasnic scored with a deflected shot in the 70th and Fabrice Muamba rounded off a swift counterattack with 11 minutes remaining.
Hill was sent off for pushing his head into Martin Petrov’s chest.
Midfielder Wes Hoolahan scored a 45th-minute equalizer for Norwich at Wigan, which had led through Ben Watson’s early penalty, and Wolves rallied at Blackburn through goals by Steven Fletcher and Stephen Ward.
Kenny Dalglish started the season as Liverpool manager for the first time since 1990 and saw Suarez put an early penalty over the bar after he had been fouled in the area by Kieran Richardson.
A bright start by Liverpool’s much-changed side continued when Suarez headed in Adam’s free kick, but Larsson volleyed in Ahmed Elmohamady’s right-wing cross to clinch an unlikely draw.
In Glasfow, Scotland, although Celtic and Rangers both won Saturday, Motherwell stayed top of the Scottish Premier League with a 1-0 win at St. Mirren.
Tom Hateley scored an injury-time free kick to keep Motherwell one point ahead of Celtic, which beat Dundee United 5-1 with goals from five different players.
Anthony Stokes, Gary Hooper, Ki Sung-yeung, Joe Ledley and James Forrest all scored to take Celtic to a maximum nine points from three matches. Motherwell has played one game more.
Rangers is two points behind Celtic in third place after American midfielder Maurice Edu scored and was sent off in the defending champion’s 2-0 win at Inverness.
Also Saturday, Hearts beat Aberdeen 3-0 and Dunfermline won 1-0 at St. Johnstone.
Luiz Gustavo scored in stoppage time to give Bayern Munich a 1-0 win at VfL Wolfsburg on Saturday, their first goal and points of the Bundesliga season, while champions Borussia Dortmund lost 1-0 at Hoffenheim.
Dutchman Klaas Jan Huntelaar hit a hat-trick as Schalke 04 came from behind to demolish hapless Cologne 5-1.
Mainz 05, who beat Freiburg 2-1 away, and Hanover 96, who won by the same score at Nuremburg, have six points from their opening two games.
Hamburg SV and promoted Hertha Berlin drew 2-2, allowing both sides to pick up their first point.
There were important, controversial refereeing decisions in three games, including Bayern’s where Wolfsburg had a goal harshly disallowed for offside.
Bayern, who suffered a shock 1-0 home defeat by Borussia Moenchengladbach in last week’s opener, were without Dutch winger Arjen Robben, who suffered a minor back problem in training on Friday.
Bayern striker Ivica Olic came on as a second-half substitute to make his first appearance for nine months following a knee operation and 19-year-old Japanese Takashi Usami made his Bundesliga debut, also after halftime.
Wolfsburg should have gone ahead when Patrick Helmes headed in from close range just after the half hour.
His effort was disallowed although replays showed he was clearly onside when a cross was played in.
Wolfsburg coach Felix Magath, whose side won 3-0 at Cologne last week, was livid at the decision and was still ranting when Bayern midfielder Toni Kroos was booked for diving in the penalty area shortly afterwards.
The game was heading for a draw until Croatian striker Olic escaped his marker on the left, found an unmarked Franck Ribery in the penalty area and the Frenchman laid the ball off for Luiz Gustavo to nonchalantly sidefoot home.
Dortmund, who began with an impressive 3-1 win over Hamburg a week ago, were beaten by an early Sejad Salihovic free kick at Hoffenheim.
The visitors had a penalty turned down when Shinji Kagawa appeared to be tripped just before the interval.
Schalke’s goal spree began with what looked to be an extremely harsh penalty awarded for handball.
It was converted by Huntelaar three minutes before halftime to wipe out Lukas Podolski’s early strike for Cologne.
