Ramsey, who will join Juventus in the summer, took advantage of some poor defending by the visitors to send a low effort onto the post and into the back of the net in the 30th minute.
The opener came after the midfielder had seen an earlier effort ruled out because of a foul by Sokratis on Florian Lejeune, but Lacazette made sure of the win against a nervy Newcastle side with a classy chip over Martin Dubravka seven minutes from time.
The victory – Arsenal’s 10th successive home win in the league – elevates the Gunners into third place and two points above Tottenham and Manchester United, although both clubs can overtake Unai Emery’s side should they beat Crystal Palace and Wolves respectively in midweek while Newcastle remain seven points above the drop zone.
Arsenal’s hopes of securing a Champions League spot had, earlier in the season, looked to be fading dream such was the consistent form of their top-four and, indeed, London rivals Tottenham and Chelsea.
But the season is a long one, and there are many twists and turns – which the Gunners have certainly found out to their benefit.
With Tottenham suffering their fourth loss in five league games at Anfield on Sunday and Chelsea who, despite being fortunate in beating Cardiff earlier on the same day, enduring a poor time on the road in 2019 Arsenal knew that a win over Newcastle would strengthen their top-four ambitions.
And the north Londoners thought they were on their way to doing just that when a corner kick was flicked on by Alex Iwobi and into the path of Ramsey, who fired the ball into the back of the net – only for referee Anthony Taylor to disallow the apparent opener.
It transpired that Sokratis had fouled Lejeune in the area in the build-up to the goal but, while the Arsenal centre-back had certainly pulled his Newcastle counterpart down, it appeared a rather soft foul.
Nevertheless, Ramsey wasn’t to be denied a second time when Matteo Guendouzi threaded a through ball into his path before sending the ball to Lacazette. The striker’s touch sent the ball rebounding off DeAndre Yedlin and back to Ramsey, who rolled in a low shot which hit the post on its way in.
The goal relieved the many disgruntled Arsenal fans sat near the press box, who hadn’t been shy at expressing their frustrations at seeing Ramsey’s initial goal chalked off.
But as Arsenal took a greater hold of the game, the tension within the stands seemed to ease and the Gunners could have given their supporters something more to cheer about when Lacazette was denied a goal in the dying stages of the first half by a superb diving stop by Dubravka.
Newcastle looked nervous particularly at the back in the first half, similar to in their 2-2 draw away to Bournemouth before the international break, and things didn’t change after the break.
Indeed, Lacazette thought he should have been awarded a penalty when Paul Dummett slid in to bock the striker’s attempted cross near the by-line only for the ball to strike his arm.
Nothing was given, and Emery changed things up by sending on Pierre-Emerick Aubameyang, who had been left on the bench with a temperature.
The striker tested Dubravka with his powerful effort from the right but, while not scoring a goal on the night, Aubameyang did get an assist after flicking the ball over Jamaal Lascelles’ head, which allowed Lacazette to chip it over Dubravka and seal the win in style.