Charlie Austin's 75th-minute penalty secured the points for Harry Redknapp's side, the striker sending Wayne Hennessey the wrong way to maintain the only unbeaten run in the division.
Their advantage at the summit is now three points after Blackpool and Leicester City fought out a 2-2 draw at Bloomfield Road.
Tom Ince's last-gasp spot-kick goal ensured that the hosts earned a share of the spoils after Paul Konchesky's penalty and Andy King's strike had eclipsed Chris Basham's opener.
Burnley took advantage of that draw to move into second place with a 2-1 win over Leeds United.
Scott Arfield and Sam Vokes put the visitors into a two-goal lead, and although Matt Smith pulled one back for Brian McDermott's side, Burnley held on to record their first win at Elland Road since 2004.
Individual performance of the day went to Birmingham City debutant Jesse Lingard after the Manchester United loanee scored all four goals in the 4-1 victory over struggling Sheffield Wednesday.
The 20-year-old scored a 13-minute hat-trick in the first half before adding his fourth in the 51st minute.
His afternoon was soured by his late substitution due to injury, but his team-mates were able to secure their second win of the season despite Kamil Zayatte's consolation goal for the visitors.
After starting the season strongly, Nottingham Forest were held to their second draw in a week against Doncaster Rovers.
Federico Macheda, on loan from Manchester United, scored twice for Paul Dickov's side, but Chris Cohen and Andy Reid earned Forest a 2-2 draw.
Watford continued their strong start to the season as they crushed Barnsley 5-1 at Oakwell.
Gianfranco Zola saw five different players find the back of the net as they moved into the top five of the Championship.
For the hosts their poor start to the season continues, and Jason Scotland's early equaliser was the only positive for David Flitcroft's side.
Reading and Brighton and Hove Albion both picked up 3-1 victories as they continue to climb up the table.
Reading's 3-1 win over Derby County at Pride Park was sealed by Nick Blackman's stoppage-time goal, while Brighton came from a goal down to beat Bolton at the Amex Stadium.
Bolton remain bottom of the table after suffering their worse start to a season in over 100 years.
Middlesbrough and Bournemouth shared six goals at the Riverside Stadium, with Jonathan Woodgate scoring a late own goal before Rhys Williams was dismissed for the hosts.
Millwall won the early kick-off on Saturday thanks to a Scott McDonald strike against Charlton Athletic, while Blackburn Rovers and Huddersfield Town battled out a goalless draw.
