Spark a revival for the Baggies
showed an impressive willingness to unpick a Swansea defence led solidly by Federico Fernandez, chipping balls into the channels with both sides of his boot, but the first real chances did not arrive until shortly before the break.
Swansea, compact but curiously reticent, should have broken the deadlock in the 40th minute after Clucas and Abraham combined to part West Brom’s centre-halves.
It fell to Andre Ayew to apply the finishing touch, but he poked at the chance and fired the balll wide.
Seconds before the whistle, the hosts produced their best effort to date – Craig Dawson nodding down Brunt’s freekick and Rodriguez stinging Lukasz Fabianski’s palms with a rasping shot.
The 28-year-old went one better 10 minutes after the restart, sniping from pointblank range to give Albion the lead.
After a goalmouth scramble, Matt Phillips provided a much-needed moment of calm, taking a soft touch to control the ball then bending a measured cross from the left wing.
Salomon Rondon rose to flick it across goal and Rodriguez stole a march of Kyle Bartley, on for the injured Mike van der Hoon, to prod home.
Rodriguez gave a tell-tale double take in the linesman’s direction, but led the celebrations as soon as he saw the flag would not be raised against him.
Rodriguez and James Mcclean seemed eager to add a second, haring into space and leading the counterattack whenever Swansea pressed forward.
Nathan Dyer’s arrival off the away bench changed the dynamic, the winger’s pace pushing West Brom back on their heels and encouraging them to surrender sit deep.
The leveller came from a corner on his side, Clucas standing the ball up and Abraham beating Livermore to power his header home and salvage a point.