The France international, who scored against Monaco on Tuesday night as Arsenal crashed out of the Champions League, broke the deadlock in the 24th minute with a close-range finish.
We knew we needed a third goal but they put us under pressure and did well to come back
Giroud took his tally to 13 Premier League goals this season four minutes later after the 28-year-old striker guided a header past Newcastle goalkeeper Tim Krul.
Newcastle halved the deficit through Moussa Sissoko in the 48th minute, but Arsenal held on to secure a fifth straight Premier League win and move to within four points of leaders Chelsea.
Speaking to BBC Sport, Giroud said: “It was a tough game but it is a really important win. Even though we are disappointed with the Champions League exit, we want to fight on until the end of the season.”
Giroud admitted that the north London side allowed their opponents back into the match in the second half, adding that a lack of a third goal made for a difficult end to the game.
“We started well, on the front foot, we put the pace we wanted to into the game,” Giroud added.
“The problem in the second half was we didn’t play, I don’t know why. We knew we needed a third goal but they put us under pressure and did well to come back.”
Giroud, who moved to Arsenal from Montpellier in 2012, has scored 13 goals in 14 Premier League starts this season.
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