Elmander's second half strikes added to a pair of penalties from Kevin Davies and a cool finish from Lee Chung-yong to move Coyle's men at least temporarily up to the dizzy heights of fourth in the table.
It wrapped up a fantastic week for Elmander whose wife gave birth to a baby girl on Thursday and Coyle said: "I knew Johan would be chomping at the bit to play and his performance was outstanding."
He added: "I'm very comfortable with the relationship I have with Johan. We speak all the time and I understand that as a player you get on a run and you don't want to be sidetracked. We'll continue to have a dialogue and it doesn't faze me."
However Coyle was keen to shrug off suggestions that his side should now be aiming at a European place after their fine run which has seen them leapfrog moneybags Manchester City on goal difference.
Coyle added: "We're enjoying the wins but the only league table I've ever looked at is the one after the season is finished. I'll see them if we've improved. Everyone is giving their all and they're doing it with a smile on their faces.
"We asked the players to give the same again and from the first whistle the level of performance was terrific. If I'm nit-picking I'm disappointed we lost a goal but Newcastle are a good side with good players.
"There is no doubt Andy Carroll is a top player at the moment and will continue to get better, but the way my players went about it they fully deserved the three points. We scored lots of goals and we could have had more."
Source: PA
Source: PA