That's four goals in five days at St James' Park for the gangly striker as Sheffield Wednesday slipped to their first defeat following two opening draws.
But this was no plain sailing for Newcastle as they had Fabricio Coloccini, Alan Smith and Steven Taylor all cautioned against the hard-working Hillsborough outfit in front of a crowd of 44,904.
The big difference was in defence where Newcastle were rock solid as they kept successive clean sheets.
Wednesday only had one real chance of any merit, a late chance for substitute Francis Jeffers that was blocked by Steve Harper.
Joey Barton failed to recover from the knock he picked up during Saturday's win over Reading which meant Ryan Taylor switched to his midfield slot on the right and there was a debut at right-back for Manchester United loan player Danny Simpson.
Wednesday were unchanged from the side that drew 1-1 at Peterborough.
Newcastle attacked from the off and Kevin Nolan finished off as fine move by driving just over.
Wednesday got back into the game and the determination of Harper and Steven Taylor was necessary to crowd out Sean McAllister, who only managed to fire high and wide under pressure.
Skipper Smith was booked after 14 minutes following a rash challenge and from the Wednesday free-kick, it was Newcastle who ultimately went ahead.
Wednesday keeper Lee Grant hit the free-kick straight at Harper who in turn launched it straight downfield where it was headed on by Andy Carroll and Ameobi superbly swept the ball beyond Grant.
Ameobi then came close to a second goal a couple of minutes later, rising well to head a Ryan Taylor corner that Grant held just under the bar.
Despite their neat and tidy approach work, Wednesday did little to trouble Harper in the half first as far too often they were let down by a poor final delivery.
Ryan Taylor, yet to open his United account, came close to doing so after 52 minutes when his 25 yard free-kick was acrobatically turned behind by Grant and from the flag-kick a Nolan thunderbolt flew just over the bar.
Carroll limped off after 58 minutes to be replaced by Xisco with United having clearly lost their first-half momentum.
Wednesday looked as if they had a goal in them and came close after 64 minutes when hard-working former Sunderland player Michael Gray's free-kick was turned behind by Harper.
Wednesday had a wonderful opportunity to draw level four minutes from time as Newcastle desperately lost their way.
A ball over the top was superbly controlled by substitute Jeffers, who worked himself into a shooting only to be denied by a brave Harper block.