Keeper Steve Harper had to pull off fine saves from Cedric van der Gun and Andrea Orlandi to preserve his clean sheet, and his replacement Tim Krul had to keep out Nathan Dyer's second-half effort and an injury time piledriver from defender Angel Rangel as the visitors enjoyed long periods of possession.
But they were not as clinical as the Magpies and it was they who eased to victory in front of a crowd of 42,616 as manager Paulo Sousa's trip to the spiritual home of the late Sir Bobby Robson, who signed him during his spell at Sporting Lisbon, ended in disappointment.
The home side were in front within eight minutes after Danny Guthrie played a corner out to skipper Alan Smith and he helped it into the middle.
Central defender Fabricio Coloccini flicked the ball on for Harewood to head firmly past stranded keeper Dorus de Vries.
Guthrie twice blocked Orlandi shots in quick succession after Harewood had impeded Harper as he tried to punch a Darren Pratley free-kick clear, and City responded admirably to the task of trying to force their way back into the game.
But it was 2-0 with 21 minutes gone when Jonas Gutierrez, not for the first time, skipped past full-back Rangel and this time delivered the perfect cross for Lovenkrands to head home.
Harewood got his second just seven minutes later with a deft near post header from Lovenkrands' cross, although it took a fine save from Harper to deny van der Gun on the half hour and a goal-line clearance from Enrique to keep out Nathan Dyer's shot seconds later.
Harper, who had to keep out a raking drive from Orlandi in injury time, failed to appear after the break and his place was taken by Krul.
The young Dutchman was protected by Steven Taylor's fine block within three minutes after the restart after Leon Britton had played Orlandi in.
Spanish midfielder Orlandi was proving a real handful, and it was he who played Dyer through with 55 minutes gone, forcing Krul to make a vital save with his legs.
Danny Simpson had to clear substitute David Cotterill's 63rd minute effort of the line with Taylor off the pitch for treatment, and the midfielder fired just wide three minutes later.
Magpies substitute Nile Ranger headed over from Lovenkrands' 80th minute cross, and for all Swansea's enterprise, they simply could not find a way past Krul and his defenders.