The boys were pinging the ball around with a fair degree of confidence in the opening 15 minutes and there were a few early groans from the home support.
In the end they went on to indulge in some time-consuming keep ball to see the game out.
There was one change to Tottenham's starting line-up. Mido was missing with a groin injury, so Jermain Defoe was on from the start, while young striker Lee Barnard was added to the bench.
Martin Jol: "We have 61 points now and I'm very proud of my players - it's exciting stuff. Our possession play was good but we made it hard for ourselves a bit by not scoring the second or third goal. We had to fight for everything but we created so many chances, with Jermain Defoe, Robbie Keane, Jermaine Jenas and, later on, Danny Murphy, so we should have won by several more goals. We couldn't do that and ended up having to take more risks by putting on three centre halves to counteract Everton's tactics. We were expecting it to be a bit tougher than it was. People who have not seen the game may think this was a narrow escape, but it wasn't. This was a very important game and we are delighted to have won at a difficult place."
Jol on Tainio's injury: "Teemu had a hamstring problem at half-time and I didn't want to take a risk."
He also confirmed Ledley King was injured, and the pair are considered very doubtful for the rest of the Easter programme.
Ledley King: "Arsenal not winning against Portsmouth in midweek gave us a boost, believe it not. We felt we could win against Everton and we stuck at our task and it was a great three points. I think we broke on them well and had the better of it, we passed the ball well and at times they couldn't get near us. There were a lot of chances for us and I don't think Robbo had to make too many saves. It was a great all round team performance by everyone involved, including the players who came off the bench. After the goal we drove on and kept getting the blocks in, picking up the ball, knowing that if we didn't concede it would be another three points."
Robbie Keane: "I thought it was a great team performance where we showed a lot of character and it was a great to have been lucky enough to get a great result and three points. The lads are very happy. It means a hell of a lot to us. I was about to pull the trigger and he pushed me a little bit. It was a penalty but at the same time, the ball did drop to Jenas and I wish the referee had waited a second longer so it would have been a goal and I wouldn't have had the pressure on myself."
"Jermain Defoe had two great shots that ended with magnificent saves and Jermaine Jenas also had a chance. We had the chances to wrap the game up but their keeper made some good saves. We were thinking towards the end that it (conceding vital late goals) has happened to us before. We defended well as a team though and Calum Davenport came on for his first game in a long time for us and he was absolutely fantastic."
David Moyes (EFC): "We have no complaints. Tottenham were the better side. They came here and showed that they are under no pressure. They are probably as good a team as we have had here at Goodison this year. If they continue to play as well as they did today they will have a very good opportunity to get the fourth spot."
Source: Official sites