Michy Batshuayi has been admitted to hospital for scans on a suspected ankle injury sustained in Borussia Dortmund's 2-0 defeat to Schalke on Sunday.
Dortmund captain Marcel Schmelzer lost possession to Caligiuri, who raided through midfield and fed the pass to Konoplyanka on the left side of the penalty area, a thumped left-footed finish giving Burki no chance.
"It's a privilege for me to be up there with the ultras", the 32-year-old Tedesco said.
Dortmund made a flying start in the reverse fixture but Schalke began on top this time around, Alessandro Schopf forcing a fine save from Burki, who got down well to his right.
The win sees Schalke go four points clear of third-place Bayer Leverkusen, with a place in next season's Champions League looking extremely likely.
"We hope that it is not so bad", said coach Peter Stöger in the post-match press conference. "Everyone knew we could devour any opponent on a good day".
Konoplyanka broke the deadlock just five minutes after the restart as he latched onto Daniel Caligiuri's pass in behind the defence and slotted past Burki.
The hosts threatened again moments later as Amine Harit lined up a shot from distance that drifted wide of the right post, while Guido Burgstaller dragged an effort to the left of the target on 13 minutes.
It had also been suggested that the injury means Batshuayi's loan at Dortmund is over and he is heading back to Chelsea for treatment.