The bronze medal match had ended goalless after 90 minutes, but Williams, England’s most capped player of all-time, calmly slotted home a spot-kick in extra-time as the Lionesses ended their Canada 2015 on a high, following their agonising semi-final defeat by Japan.
It was the first-ever time England had beaten Germany, FIFA's No1-ranked side, after 21 attempts, and it means they left the World Cup as the best-placed European team.
By finishing third, Mark Sampson's side became the second-most successful England team of all-time, behind the famous 1966 squad - and they earned legions of new fans in the process.They had already made history by being the first England Women's team to win a World Cup knockout match. They bettered that by reaching their maiden semi-final.
And by claiming a podium finish in Edmonton they ensured their names will be forever etched in English football history.
The nation’s new heroes began with a back three of captain Steph Houghton, Laura Bassett and Jo Potter, who was making her first start of the tournament, while full-backs Lucy Bronze and Alex Greenwood offered support from their more advanced positions out wide.
In an eventful opening at the Commonwealth Stadium, Karen Bardsley was forced to turn behind Lena Petermann's near-post header for a corner after just 37 seconds.
Celia Sasic, who scored two against England at Wembley in November, then shot tamely when put through by Melanie Behringer. And just moments after shrugging off a knock, Houghton executed a crucial goal-line clearance to hook away Potter’s mis-directed header.
England’s first opportunity fell to the skipper, but she couldn’t get enough contact on Bronze’s low cross and Nadine Angerer gathered in the Germany goal.
The game settled down somewhat in terms of chances, though the Lionesses got stronger as the first half went on against their illustrious opponents – and only had two more efforts to survive, from Sara Daebritz and Sasic, before the break.
After the heartbreak of scoring the now-infamous added-time own goal against Japan, Bassett vowed to bounce back, and she didn’t put a foot wrong in the opening 45 minutes, with Opta stats showing she completed every one of her 20 passes.
Bardsley, player of the match in the last-16 win over Norway and again here in Edmonton, produced one of her best saves of the tournament early in the second half, when she flung to her right to palm away Daebritz’s 10-yard volley.
If the first half was relatively cagey, things certainly opened up in the second period as Katie Chapman and Jill Scott headed wide from corners and then Tabea Kemme drilled a shot off target from the edge of the England box.
Williams fired a shot in from distance which was blocked by Bianca Schmidt and Greenwood couldn’t quite capitalise on the rebound.
Scott then found herself free inside the box when played in by substitute Eniola Aluko, on for White, but the midfielder dwelled on the ball, which forced play to go out wide to Karen Carney. The cross back in was dangerous but Scott couldn’t stretch her long legs enough to reach it.
Aluko had a good chance herself towards the end, when she raced clear into the box. But her cushioned header was too heavy and Angerer came out to foil the Chelsea striker at her near post.
England were on top in the closing stages but couldn’t find a breakthrough – and they were indebted to Bassett for making a last-ditch sliding tackle on the halfway line to deny Germany a clear chance to counter-attack in the 91st minute.
The only action of note in extra-time gave England their bronze medal when Lianne Sanderson, on for Chapman, was brought down inside the box by Kemme.
Williams stepped up to slide home the spot-kick to Angerer’s bottom right – the same place her other two penalties went, against Colombia and Japan.
There was one huge let-off for England in the closing stages, though, when Schmidt headed wide at the back post when totally unmarked.
But they were due a bit of luck in this tournament – and they held on gamely for bronze.
The Lionesses’ Canada 2015 campaign was one that captured the hearts of the English public.
As Sampson’s side roared into the knockout stages, past the host nation and into a first-ever semi-final, goodwill messages came flooding in from Prince William, David Beckham, Wayne Rooney and a number of other household names.
The messages that meant the most to the 23 players were the ones that said they had inspired young girls to go out and buy a pair of football boots for the first time.
But they did not just inspire young girls. They inspired a nation.
England (3-4-3): 1 Karen Bardsley (Manchester City); 5 Steph Houghton (capt; Manchester City), 6 Laura Bassett (Notts County), 17 Jo Potter (Birmingham City); 12 Lucy Bronze (Manchester City), 4 Fara Williams (Liverpool), 16 Katie Chapman (Chelsea), 14 Alex Greenwood (Notts County); 8 Jill Scott (Manchester City), 23 Ellen White (Notts County), 10 Karen Carney (Birmingham City).
Substitutes: 9 Eniola Aluko (Chelsea) for White 61, 20 Lianne Sanderson (Arsenal) for Chapman 80, 15 Casey Stoney (Arsenal) for Williams 111
Substitutes not used: 2 Alex Scott (Arsenal), 3 Claire Rafferty (Chelsea), 7 Jordan Nobbs (Arsenal), 11 Jade Moore (Birmingham City), 13 Siobhan Chamberlain (Arsenal), 18 Toni Duggan (Manchester City), 19 Jodie Taylor (Portland Thorns), 21 Carly Telford (Notts County), 22 Fran Kirby (Reading).
Goal: Williams (pen, 108)
Bookings: Chapman 77, Bardsley 83, Bassett 92
Head coach: Mark Sampson
Germany: (4-4-2): 1 Nadine Angerer (capt); Bianca Schmidt, 14 Babett Peter, 3 Saskia Bartusiak, 22 Tabea Kemme; 6 Simone Laudehr, 20 Lena Goessling, 7 Melanie Behringer, 23 Sara Daebritz; 13 Celia Sasic, 19 Lena Petermann.
Substitutes: 16 Melanie Leupolz for Behringer ht, 11 Anja Mittag for Sasic 73, 18 Alexandra Popp for Goessling 101
Substitutes not used: 4 Leonie Maier, 5 Annike Krahn, 8 Pauline Bremer, 9 Lena Lotzen, 10 Dzsenifer Marozsan, 12 Almuth Schult, 15 Jennifer Cramer, 17 Josephine Henning, 21 Laura Benkarth
Head coach: Silvia Neid
Referee: Hyank Ok RI
Attendance: 21,483
