Headers from Sturridge, Lallana and Cahill gave the interim England boss the points at Wembley on Friday evening.
England remain top of World Cup qualifying Group F thanks to a 3-0 victory over Scotland at Wembley on Friday.
Goals from Daniel Sturridge, Adam Lallana and Gary Cahill secured three points for Gareth Southgate’s side, despite a rather unconvincing display from the hosts for much of the encounter.
Pre-match talk had been dominated by a dispute with FIFA over their refusal to allow the teams to wear poppies on their shirts, and, as expected, both sets of players wore black armbands bearing the symbol in recognition of Armistice Day.
England – who had captain Wayne Rooney restored to the starting line-up – had looked unsteady against a Scotland side still smarting from a 3-0 loss to Slovakia last time out, until Sturridge’s clever header put them ahead on 24 minutes.
Gordon Strachan’s side missed two excellent chances to level before Lallana steered in a Danny Rose cross just after half-time, and England’s control of the game was made certain when Cahill nodded in from a corner.
Though the performance was far from inspired, a second win in three games under interim boss Southgate will likely increase the calls for him to be given the job on a full-time basis, with England two points clear at the top of the group and on course to reach the 2018 finals.
For Scotland – who have four points from four games and only one win in their last six – the future of Strachan now looks more uncertain than ever.
Loud boos rang around Wembley for the respective national anthems, but both sets of fans observed a meticulous minute’s silence, with many in the stands wearing plain white t-shirts emblazoned with the poppy emblem.
Scotland settled the better of the two teams, with John Stones looking particularly unsteady for a stuttering England, but Sturridge gave the home side the lead with the first real opportunity.
Raheem Sterling’s blocked shot found its way to Kyle Walker, and his low cross was brilliantly steered into the near corner of the net by the head of the Liverpool striker.
Stones made a good block to deny Leigh Griffiths, before Grant Hanley drifted away from the Manchester City man at a corner only to head over the crossbar, as Scotland pushed for a swift response at the end of a half in which they performed far better than they did at any stage of that Slovakia defeat.
Scotland started the second half firmly on the front foot but they wasted two superb chances to level the match. James Forrest dragged a shot wide from a promising opening, before Stones stuck out a leg to deny Robert Snodgrass from close range within just four minutes of the restart.
Strachan’s frustrations on the touchline were clear, but matters only got worse for the under-pressure coach when England snatched a second less than a minute later. Sturridge found Rose down the left and his cross was met by the unmarked Lallana, who steered a fine header beyond Craig Gordon from 12 yards.
England at last looked to be in control, and they made certain of the points on the hour mark, as Cahill headed in Rooney’s corner despite Gordon getting a hand to the ball.
Anger among the visiting fans boiled over as objects, including a water bottle, were thrown onto the pitch close to Joe Hart’s goal, but further Scottish blushes were spared when Sterling somehow contrived to shoot over the crossbar from barely a yard out.
Sterling almost teed up substitute Jamie Vardy for a fourth, but England saw out the closing moments in comfortable fashion to make it three wins from their last three clashes with their neighbours, putting three past Scotland for the third game in succession.