Goalscorer Williams also went close with two headers
A goal by Everton midfielder Fara Williams gave England their 19th victory in 20 meetings with Scotland.
But a team showing nine changes from Thursday night's 6-0 win against Russia struggled at times against a battling Scottish side.
The fluency shown against the Russians was never in evidence in a largely disjointed display.
And in the second half, Scotland twice went close to cancelling out William's 30th-minute goal.
With Williams to the fore, however, England bossed the first half.
The Everton player had a sixth-minute header cleared off the line by Hibernian midfielder Kirsty McBride.
She then went close again when her 16th-minute header flew inches over the bar.
But she was bang on target on the half-hour, directing a 40-yard lob over back-peddling goalkeeper Gemma Fay and into the roof of the net.
Soccer Locker midfielder Ifeoma Dieke wasted a close-range equalising chance three minutes later.
But at the other end, either side of half-time, wingers Alex Scott and Sue Smith sent shots just wide of the post.
The Scots began to take control midway through the second half, however.
And England had a narrow escape when Arsenal striker Julie Fleeting's 68th-minute free-kick was pushed on to the bar by substitute goalkeeper Carly Telford.
Telford pulled of an even better save five minutes later, diving to turn McBride's 15-yard drive past the far post.
But the visitors' challenge faded in the closing stages and Sunderland right-back Steph Houghton almost stretched England's lead with an 83rd-minute volley over the bar.
England: Chamberlain (sub: Telford HT); Houghton, Bassett, Phillip, Unitt (sub: Yorston 78), Williams, J. Scott; K. Smith (sub: Chapman HT), A. Scott (sub: Johnson 78), Sanderson (sub: Barr 59), S. Smith (sub: Potter 59).
Scotland: Fay; Jones, Ross (sub: Sommerville 84), Dieke, McDonald, Love, Burns, McBride (sub: Brolly 81), Sneddon (sub: Little 57), Fleeting, Hamill (sub: Malone 66).
Referee: M P Russell