A dominant first half from Newcastle in terms of possession saw the sides go in goalless at the break.
The Magpies then found the breakthrough 10 minutes into the second half as Joelinton’s cross was turned into the Arsenal net by defender Ben White as Callum Wilson tried to connect.
Guimaraes then pounced on a Aaron Ramsdale save to make it 2-0 late on.
The win sees Newcastle move up to 46 points for the season, their highest points tally since returning to the top flight in 2017.
Eddie Howe made two changes to the side that were beaten 5-0 at Manchester City last weekend with Fabian Schar and Wilson coming back into the side in place of Jamaal Lascelles and the injured Chris Wood.
Wilson was named Newcastle captain for the evening in what was his first start for the club since December 27.
Here are our Newcastle United player ratings from the match...
1. Martin Dubravka - 6
Was rarely tested in between the sticks but dealt with what little came his way well. Photo: Stu Forster
3. Fabian Schar - 7
Was calm and composed at the back before being forced off with a head injury early in the second half. Photo: George Wood
4. Dan Burn - 8
Made two great blocks in the first half and kept Arsenal at arm’s length as they tried to get back into the game. Photo: Ian MacNicol