Federico Fernandez's own goal set the Blues on their way, the Argentine defender poking the ball over his own line while under pressure from Ben Chilwell.
But Abraham made sure of the points with a smart finish following Werner's pass after Newcastle had threatened through Isaac Hayden and Joelinton. Sean Longstaff hit the bar for the home side towards the end.
Abraham said: "It's a fantastic result, we had to dig deep as it's never an easy place to come. It was 1-0 for a very long time, they created a few chances, but so did we, but we defended well and got that second goal.
"We didn't let didn't the international break distract us, we had to come to come out all guns blazing, we did that and it's a massive three points.
"These games are always tricky when you can't get that second goal. It's very easy to drop your head and lose confidence, but we didn't do that and kept going.
On his goal, he added: "We knew we had to be quick on the counter so I had to get myself forward. I was tired but I had to keep control and it killed the game off thankfully."
And on being top of the table, Abraham joked: "No pressure! That's where want to be, we just need to keep getting the three points and hopefully we will stay up there."