Chelsea Weston, Remi Allen, Kirsty Linnett, Jo Potter and Melissa Lawley all returned to the side after sitting out the 0-0 draw with Everton on Wednesday, whilst Brazilian striker Marta was passed fit for the visitors having reportedly been a doubt with a hamstring injury.
This was the third game in six days for the hosts and they were a bit slow out of the blocks as Tyreso dominated early possession. The visitors could have taken the lead after six minutes when a corner was only half cleared by Blues' Jess Carter and captain Caroline Seger's scuffed shot found Marta six yards out, but the five-time FIFA Women's Player of the Year winner could only curl her effort wide.
The Brazilian had an ever better opportunity four minutes later when she latched on to a punted ball over the top, but her left-footed drive squirmed past the post.
With 17 minutes on the clock, Tyreso should have taken the lead when striker Veronica Boquete cut inside from the right-flank, but her left-footed effort from 12 yards clipped the post as it went wide.
From there on in, Blues settled in to the game and began to have more possession - particularly captain Karen Carney who had the regular beating of her marker Line Roddik. It was to be a day of fine margins and Carney twice almost slipped in Linnett, only for her passes to be cut out at the last moment.
With three minutes of the second half gone Blues suffered a blow as Kerys Harrop was booked for handball, a decision that rules the centre-half out of the second leg in Sweden.
Tyreso started the second half as they did the first and had a lot of the ball but were failing to create any clear-cut chances, which was testament to the home defence - in particular Aoife Mannion - who were blocking efforts from all angles.
With that in mind, it was surprising that it took until three minutes past the hour mark for home goalkeeper Rebecca Spencer to have to make save, palming away Marta's sweetly-struck 30-yard free-kick.
Jade Moore almost showed the Brazilian how it is done two minutes later. After wriggling away from her marker the England international rifled a 25-yard effort inches wide of the post.
As the second half went on, it was Blues who looked the more dangerous side and they were having lots of success from the wings and Lawley's effort was blocked after she had superbly rolled Meghan Klingenberg.
But the visitors were quick to remind the 1,580 watching fans of their ability and Christen Press really should have scored when she was picked out by Roddick, but the striker put her effort over the bar from 18 yards.
With nine minutes to go, Blues had their best opportunity. Moore seized on to a loose ball in the Tyreso half and exchanged passes with Carney to find space on the edge of the box, but her left-footed effort went wide as her route to goal opened up.
Blues had a succession of late corners as they pushed for a goal to take to Sweden. That was not forthcoming, but denying the visitors a crucial away goal was equally important and Blues will look to score at least one of their own in next week's second leg.
Blues Ladies: Spencer; Weston, Mannion, Harrop, Carter; Moore, Potter; Carney, Allen, Lawley; Linnett.
Subs: Baggaley, Sargeant, Keryakoplis, Simpkins, Westwood, Wilkinson, Torkildsen.
Tyreso: Soberg, Engen, Roddik (Edlund, 87), Dahlkvist, Boquete, Marta, Diaz (Rilany, 87), Press, Seger, Sembrant, Klingenberg.
Subs: Korpela, Klinga, Thaisa, Rytting Kaneryd, Mayara.