A Robert Mak double secured Slovakia their first win of 2018 World Cup qualifying with a 3-0 victory over Scotland in Trnava.
Mak struck once either side of half-time, with Adam Nemec's second-half header giving Slovakia all three points against the insipid visitors.
The winger's first came in controversial circumstances as he fired home the rebound from a David Marshall save, after the recalled Steven Fletcher appeared to have been fouled at other end of the field in the lead-up.
An emphatic finish from Mak and a towering Nemec header in the second period intensifies pressure on Scotland manager Strachan following their 1-1 stalemate with Lithuania at the weekend.
Strachan was incensed with the nature of the hosts' first goal, but it was a deserved defeat to a side who had not scored in four previous internationals.
Scotland must now travel to group favourites England next month to try and get their Group F campaign back on track, while Slovakia's confidence will be boosted ahead of a home match against Lithuania.
The visitors had carved out the first opening after 11 minutes, and probably should have taken the lead when Robert Snodgrass found Fletcher in the area with a delightful chipped pass, but the striker miscued his header wide.
It was the hosts who made the breakthrough after 18 minutes in controversial fashion. Scotland wanted a free-kick for a push on Fletcher, but referee Martin Strombergsson waved play on and while Stachan's men protested, Slovakia counter-attacked.
Marek Hamsik's initial header from a cross from the left was parried by Marshall, but Mak was there to slam the rebound into the roof of the net.
That perceived injustice spurred Scotland into action, and two minutes later they almost equalised through Snodgrass, but his effort when one-on-one with Matus Kozacik was weak and easily saved.
After that, Slovakia were happy to sit on their advantage and look for opportunities to extend their lead on the break.
While Scotland dominated possession they couldn't force any openings, and Marshall kept his team in the contest with a pair of fine saves five minutes from half-time, first tipping away a curling Mak strike, then getting down low to save Jan Durica's drive from the subsequent corner.
Slovakia extended their lead 11 minutes after the restart, with Mak grabbing his second of the game. He had some lacklustre Scotland defending to thank for it, the winger gifted space to take a touch from Jakub Holubek's cross inside the area, shimmy past Russell Martin and power home.
Mak could have completed a hat-trick minutes later, but his flashed drive across the box was palmed away by Marshall.
But it was 3-0 to Slovakia with 22 minutes to go as more poor Scotland defending allowed striker Nemec to rise and power in a header from a corner.
Substitute Leigh Griffiths made an impact when he came on, and fired inches wide, but it wasn't anywhere near enough to salvage a result for Scotland.