Charlie Hodgson's try from charged-down kick ultimately proved the difference on an evening at Murrayfield when Scotland had enough chances to win it.
England had to hold them out at the end and Lancaster put defensive effort down to the new culture he has worked to build in the squad.
"This is a very difficult place to come and win. It has been a great result for us," interim head coach Lancaster said.
"We have been delighted with the attitude we showed, particularly in defence. Our discipline was very good and our desire to work hard, play for each other, play for the shirt.
"They are the things we have talked about and it was great to see them come through
"We have talked a lot about work rate, working hard for each other and fostering a spirit and it showed on the field.
"We didn't get everything right but we got a lot of things right. We are delighted to come here and get started
"Overall it was that sense of collective spirit to play for each other and keep working and working.
"To get the try (in the first minute of the second half) was very important. It gave us a foothold on game that allowed us to grow in confidence.
"Owen (Farrell) kicked the penalty at the end which was nerveless to give us that buffer but we had to work right to the end with Scotland's passion and tenacity."
The central theme of Lancaster's tenure has been to restore a sense of pride in representing England that he felt had been lost at the World Cup.
Chris Robshaw lifted the Calcutta Cup on only his second Test appearance while seven players made the England debuts, including three in the starting team.
"It was a tremendous effort from all the guys," Robshaw said.
"Whenever you play away from home you don't have as much ball as you would like but everyone defended for their lives and it really showed what it means to each other, how proud we are to play for each other and for the nation."
England made 142 tackles to Scotland's 62 and rode their luck at times. Greig Laidlaw was unable to ground his chip forward and Ross Rennie blew a try-scoring opportunity by delaying his pass for a split-second too long, allowing Ben Foden to make the cover tackle.
They were familiar failings for Scotland, who have not scored a try in four matches and have managed only 20 in the 25 Tests since Andy Robinson took charge.
England weathered the storm and grew in confidence from the moment Hodgson charged down Dan Parks' kick to put them ahead seconds after the restart.
"Scotland threw everything at us. We held our lines and we were still in the game," said coach Andy Farrell.
"When you look at the whole two weeks, we talked a hell of a lot about culture, we keep saying this group is tight and you saw that in the last 20 minutes.
"It wasn't perfect and Scotland broke us a couple of times but the way we scrambled back and fought for each other was there to see."
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