It was a game full of chances, with Raheem Sterling coming closest with a volley against the crossbar, but honors remained even on what was billed as a special day for several members of the Reds’ setup.
The result extends Liverpool’s unbeaten run in the Barclays Premier League to eight games but keeps them in the bottom half of the table.
The team news saw Rodgers make seven changes from the side that drew with Young Boys on Thursday, although Stewart Downing and Jordan Henderson retained their places to make their second and first Premier League starts of the campaign, respectively.
Both sides created chances in an entertaining first half, although Liverpool looked to be the likelier scorer.
Sterling displayed superb technique to half-volley against the crossbar from the edge of the box, while Jose Enrique directed a Luis Suarez cross into the net only to have his celebration halted by an offside flag.
Enrique was guilty of missing from six yards after storming into the box to meet an excellent cross from Glen Johnson, whose performance in the first half was as good as you’ll see from a fullback. The England man almost found himself on the scoresheet after a one-two with Enrique, but Gerhard Tremmel was off his line quickly to scoop over the crossbar.
At the other end, Wayne Routledge forced Pepe Reina into a reflex save, while Pablo Hernandez proved a real threat and twice came close with shots from distance.
Hernandez was first to probe in the second half with a curled free kick into the stands as Swansea upped its game. There was then an escape for those in red when Joe Allen cleared an Ashley Williams header off the line.
Suarez stung the palms of Tremmel with a vicious hit after fine work from Steven Gerrard, but Swansea now had the momentum. Nathan Dyer caught out Downing before Reina came to the rescue, making himself big to block the substitute’s shot.
Rodgers acted, swapping Henderson and Downing for Joe Cole and Jonjo Shelvey.
Liverpool had a great chance to win it late when Sterling and Suarez found themselves running at just one defender. Sterling overcooked his pass, leaving Suarez with more work to do than should have been necessary. The shot was eventually saved.
Reina did well to keep out a Hernandez free kick with time running out, while Shelvey drew a save from Tremmel in what proved to be the final chance of note.
Liverpoolfc.com journalists’ man of the match: Glen Johnson.