Suarez stoops low to give Liverpool the lead after missing from the spot early on
Sebastian Larsson scored a superb volley on his debut to earn a point for Sunderland at Liverpool.
The hosts will curse the fact Luis Suarez missed an early penalty when he was tripped by Kieran Richardson before sending his spot-kick way over.
But the Uruguayan shrugged off his disappointment to nod in a 12th-minute opener from Charlie Adam's cross.
Sunderland rarely threatened in the first half but Larsson's 57th-minute goal capped a better defensive display.
Once they had equalised, the Black Cats looked the more likely victors as Liverpool ran out of steam.
And it was an impressive second-half turnaround for Steve Bruce's men, who would have been happy to take a point back to the north east after coming under serious pressure in the first period.
Dalglish looking for Liverpool improvement
With four Liverpool players making their debuts, there was lots of encouragement for Kenny Dalglish and his decision to use Suarez was entirely justified despite the striker only returning to training on Monday following his Copa America exploits.
Yet he was sprightly enough to earn the penalty in the first place, charging down Richardson's pass near the halfway line and racing clear, only to be tripped by the left-back as he shaped to round keeper Simon Mignolet.
The Sunderland defender looked fortunate not to earn a red card from referee Phil Dowd, but before the Black Cats could regroup they were behind when Adam's free-kick from the right was tucked in by the Uruguayan following Wes Brown's foul.
Guy MowbrayBBC Match of the Day commentator
It was an absolutely tremendous first half for Liverpool but in the second half they lacked a bit of spark. Steve Bruce's team did well in the second period and if there is a better finish in the Premier League this afternoon than Sebastian Larsson's volley then I can't wait to see it
Adam looked extremely comfortable during his first game in the centre of Liverpool's midfield.
And his range of passing more than made up for Steven Gerrard's absence through injury, with the former Blackpool player going close with a rasping drive.
Although Sunderland were timid early on, debutant Larsson caused Pepe Reina problems from his set-pieces, with the Spanish keeper saving from Brown's header before looking shaky on another occasion.
Three of Liverpool's four-man midfield were making their first appearances for the hosts, with Dalglish preferring Jordan Henderson, up against his former club, on the right-hand side of midfield to Dirk Kuyt.
Although Downing was deployed on the left, he almost marked his debut with a superb goal from the opposite flank on 34 minutes.
Cutting in, he raced past several Sunderland defenders to smash a shot against the bar.
Sunderland's 'deserved' draw pleases Bruce
Despite some occasionally rash challenges by both sides, the hosts were coasting and it wasn't until after the break that Steve Bruce's team improved. They had to.
It was Larsson who turned their pressure into something more tangible when he volleyed in from Ahmed Elmohamady's right-wing cross.
The Swede was given lots of room at the back post by Liverpool right-back John Flanagan but even so it was an expert finish.
After a relatively quiet first period Andy Carroll began to get on the end of more of Liverpool's crosses, but even though Kuyt was introduced in place of Henderson, the fluency ran out of their play.
Sunderland were working harder and with Suarez being withdrawn with 15 minutes to go, there was little danger behind their defence and a more evenness to the match.
a controversial goal last season
, Bruce would have been content to finish the game in relative comfort, but for both sides there were encouraging signs from their new-look players.
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