The only real concern for Hodgson was the departure in the first minute of Manchester City midfielder Fabian Delph, who was substituted with an apparent hamstring problem.
Switzerland continued to threaten, but Kane's introduction had the desired effect as the striker struck 23 minutes from time.
Rooney found Shaw, whose fine cut back found Kane and the Spurs ace drilled in his third goal of a fledgling international career.
England were ahead, but by no means clear of danger.
Smalling pulled back Shaqiri and was spared a greater punishment than a booking as Cahill was covering.
The impressive Shaw next outmuscled substitute Breel Embolo when Switzerland were pressing before Shaqiri shot wide across goal.
England were awarded a penalty when Sterling was felled by Lichtsteiner.
Referee Gianluca Rocchi had no hesitation in pointing to the spot and immediately home supporters chanted "Rooney, Rooney".
The England captain did not disappoint his expectant public, firing into the top corner, the power of the kick beating Sommer.
His celebration was one more of relief and Rooney will now look ahead to further goals for England, beginning with the October 9 clash at home to Estonia.
Wayne Rooney: Five of the best
Wayne Rooney has overtaken Sir Bobby Charlton's scoring record with his 50th England goal against Switzerland.
We look at five of his most memorable goals for England.
England 2 Denmark 3 (November 16, 2003)
Rooney, then an 18-year-old Evertonian, gave Manchester United fans a glimpse of his potential with a stunning goal in a friendly against the Danes at Old Trafford. The striker raced from the halfway line past two markers before firing in off the underside of the crossbar from 20 yards.
England 4 Croatia 2 (June 21, 2004)
England needed just a draw to qualify for the second round of the European Championship finals in Portugal, but they went behind to Niko Kovac's early strike. Paul Scholes equalised and Rooney then swung the game beyond Croatia with a 25-yard drive.
England 3 Argentina 2 (November 12, 2005)
Rooney was the best player on the pitch in what was one of the most fiercely-contested and enthralling friendlies in living memory. The then 20-year-old harassed the Argentina defence all night and got the goal he deserved in the 38th minute when he latched on to David Beckham's flick-on and slotted the ball into the corner to equalise Hernan Crespo's opener.
England 1 Ukraine 0 (June 19, 2012)
After sitting out the first two matches of Euro 2012 due to suspension, Rooney delivered on his return, bundling home at the back post to send England through to the second round.
Brazil 2 England 2 (June 2, 2013)
England were given the honour of being the first national team to visit the newly-rebuilt Maracana in Rio de Janeiro for a friendly - and Rooney scored a goal worthy of the occasion. With the score at 1-1, Rooney picked the ball up in the Brazil half and strolled towards goal before unleashing a 25-yard drive that flew right into the top corner.
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