In a competitive and hard fought game with few clear-cut openings, Manchester City forward Kosovare Asllani was presented with the best opportunity to earn her side victory from 12 yards – but Chamberlain dived low to her left to palm the ball away.
Mark Sampson’s side, who are preparing for the Euro 2017 finals, put in a much-improved performance from Sunday’s 1-0 defeat by Norway.
Sweden threatened on occasion, especially after the break and might have sneaked the win, but England controlled possession for large spells, lacking match sharpness and a cutting edge in the final third.
There were 10 changes from the Norway game, with only Liverpool keeper Chamberlain retaining her place.
Millie Bright made her first start for the Lionesses, Gemma Bonner was included for the first time since 2015 and Rachel Williams made her first start since the successful Cyprus Cup campaign in 2013.
With England hitherto on top, Stina Blackstenius thought she had put Pia Sundhage’s side ahead just before the half-hour mark when she headed home Sofia Jakobson’s right-sided cross, but the assistant referee’s flag was raised for offside.
Sweden had two FA WSL players on display in Asllani and Chelsea goalkeeper Hedvig Lindahl – and Lindahl was on-hand to save England’s first shot on target, a free-kick by Blues club mate Karen Carney.
The Scandinavians made two changes at the break with Pauline Hammarlund and Lotta Schelin replacing Blackstenius and Sofia Jakobson.
And Hammarlund forced a good save from Chamberlain when heading Jonna Andersson’s left-sided cross on target from five yards out.
She came close again when latching onto Schelin’s low centre but guided her shot just wide of the far post.
Then came Chamberlain’s champagne moment.
Sweden launched a counter attack after Williams’s fierce shot was charged down by Nilla Fischer, with shouts for hand ball ignored by the referee. The ball found Schelin who broke into the box only to be tripped by the recovering Flaherty, this time the official pointed to the spot.
Asllani stepped up to take the penalty but Chamberlain got down low to her left to ultimately earn her side a deserved draw.
England are next in action at the SheBelieves Cup in March where they will face the top three sides in the world in Germany, France and host nation – and World Cup holders – USA.
Line-ups
Sweden: 1 Hedvig Lindahl, 2 Jonna Andersson, 3 Linda Sembrant, 5 Nilla Fischer, 7 Lisa Dahlkvist, 9 Kosovare Asllani, 10 Sofia Jakobson, 11 Stina Blackstenius, 15 Jessica Samuelsson, 17 Caroline Seger (C), 18 Fridolina Rolfo.
Substitutes: 19 Pauline Hammarlund for Jakobson ht, 8 Lotta Schelin for Blacstenius ht, 6 Magdalena Eriksson for Dahlkvist 65, 14 Hanna Folkesson for Sembrant 65, 16 Hanna Glas for Asllani 80, 22 Olivia Schough for Andersson 80.
Substitutes not used: 12 Hilda Carlen.
Head coach: Pia Sunhage
England (3-4-3): 1 Siobhan Chamberlain (Liverpool); 4 Gemma Bonner (Liverpool), 5 Gilly Flaherty (Chelsea), 6 Millie Bright (Chelsea); 2 Rachel Daly (Houston Dash), 7 Isobel Christiansen (Manchester City), 8 Jordan Nobbs (capt; Arsenal), 3 Claire Rafferty (Chelsea); 10 Jill Scott (Manchester City), 9 Rachel Williams (Notts County), 11 Karen Carney (Chelsea).
Substitutes: 15 Gemma Davison (Chelsea) for Rafferty 55, 17 Demi Stokes (Manchester City) for Carney 70, 16 Steph Houghton (Manchester City) for Flaherty 80.
Substitutes not used: 12 Jade Moore (Notts County), 13 Mary Earps (Reading), 14 Hannah Blundell (Chelsea), 21 Sophie Baggaley (Birmingham City).
Bookings: Flaherty
Head coach: Mark Sampson
Referee: Marte Soro
Source: with thanks to TheFA.com
Images: FA via Getty