Accrington battled well against their Premier League opponents and went in level at the break after a wonderful effort from Ray Putterill cancelled out Taylor's equally impressive opener.
But the Magpies moved two goals ahead in the second half thanks to finishes from Ameobi and Lovenkrands before Sean Hessey's late consolation for the League Two outfit.
Newcastle boss Chris Hughton named an entirely different starting line-up from the one which had beaten Aston Villa 6-0 on Saturday, with Ameobi captaining a side which featured youngsters James Tavernier, Tamas Kadar, Shane Ferguson, Ryan Donaldson and Kazenga LuaLua.
There was a slight delay to the kick-off after fans threw shredded paper onto the pitch, but it was a lively start once things got under way.
Lovenkrands looked to take advantage of a weak defensive header back towards Ian Dunbavin in the second minute, but goalkeeper Ian Dunbavin dived on the ball to avert the danger.
At the other end, James Ryan's shot did little to trouble Newcastle stopper Tim Krul and the Premier League side were soon back on the attack, with Nile Ranger earning a free-kick after being clattered by Charlie Barnett which Taylor hit into the wall.
In the space of a few minutes Dunbavin did well to save Lovenkrands' header, Donaldson drilled wide and Ameobi nodded a corner high over the bar.
The Magpies skipper then twisted and turned in the box before unleashing a shot which was blocked.
The visitors had produced virtually all the forward play, but they were almost caught out at the back when Krul got his timing wrong as he rushed out and was fortunate to see the ball cleared away.
Newcastle then created their best chance yet as Ranger headed Taylor's corner towards goal, but Andrew Parkinson was on hand to clear off the line.
Haris Vuckic, another youngster brought into the side by Hughton, was next to try his luck but his low effort lacked power.
Ranger showed far more menace with a snap-shot after connecting with LuaLua's cross, but Dunbavin again got down to save.
The goalkeeper was well and truly beaten in the 36th minute though as Taylor fired the ball into the top corner from 25 yards to put Newcastle ahead.
It was a blow for the hosts, but Accrington refused to crumble and found an equaliser in first-half stoppage time as Putterill curled a beauty past Krul.
Stanley had their tails up and emerged after the restart looking as if they believed a giant-killing was within their grasp.
The Magpies could only partially clear a free-kick from Sean McConville in the 47th minute and the ball fell to Barnett, who fired a strike off-target.
The home supporters were lifted by their side's momentum, but only a minute later, Newcastle were ahead again as Lovenkrands headed to Ameobi, who poked the ball beyond Dunbavin.
Accrington's players complained that there had been an infringement in the build-up, but referee Robert Shoebridge judged the effort should stand.
Shortly after, it should have been 3-1 as Dunbavin's save from Ameobi fell to Ranger, but the striker saw his shot blocked on the line.
It did not take long for the goal to come though, and Lovenkrands extended Newcastle's advantage by hooking the ball in with a little over 20 minutes remaining.
Ranger then shot wide as the floodgates threatened to open, but Accrington refused to lie down and came close to pulling a goal back with a quarter of an hour to go.
First Krul tipped Ryan's shot around the post, then Phil Edwards was denied from the corner that followed and finally Putterill attempted one from distance which went well over.
Putterill looked set to net his second moments later as he met Parkinson's cross, but Krul once again kept Stanley at bay.
LuaLua was then inches away from making it 4-1 with a strike that came back off the post and Sean Hessey rifled in at the death, but it was too late for the hosts to salvage anything.