In-form Schalke 04 left 10-man Hearts without a point from two games in Uefa Cup Group A, thanks to a single, second-half strike from Cassio Lincoln.
Hearts had matched the German side until midfielder Patrick Kisnorbo was sent off shortly after the break for a second yellow card at Murrayfield.
Efforts from Ailton and Niels Oude-Kamphuis struck each Hearts post.
And pressure told when Lincoln's 25-yard drive deceived goalkeeper Craig Gordon to give Schalke victory.
John Robertson had been forced to do without injured midfielder Phil Stamp, while striker Mark de Vries was only fit enough for the bench, as the new head coach's first starting line-up was unchanged from Saturday.
Schalke arrived on a high, having moved into second place in the Bundesliga at the weekend.
And Brazilian striker Ailton gave Hearts an early warning of his vision, with a chipped snap-shot from 22 yards that might have caught Gordon off his line if it had not been a yard over the bar.
But Hearts started brightly and Jamie McAllister's drive was deflected against goalkeeper Rost by Paul Hartley and the ricochet off the Hearts midfielder skidded wide of the post.
Schalke began to dominate possession and Ailton flashed a shot across the face of the Hearts goal from an angle and then sliced another shot over on the turn.
Lincoln forced Gordon to turn a 20-yard curling effort round the post at full stretch.
Hearts were reduced to 10 men two minutes into the second half.
Kisnorbo, already booked for a foul, received a second card after referee Nikolai Ivanov decided he took a dive inside the Schalke box.
Robertson withdrew striker Ramon Pereira and brought on midfielder Neil Macfarlane as he attempted to compensate.
But the ball fell kindly to Ebbe Sand and his shot from 10 yards struck the inside of the post before bouncing clear.
The other post was also rattled by a cross from Oude-Kamphuis that deceived Gordon.
Ailton was found by the midfielder's next cross and only a fine goal-line save by Gordon prevented the Brazilian's header from 12 yards breaking the deadlock.
Joe Hamill had a chance to give Hearts a surprise lead when a long Robbie Neilson throw fell at his feet, but the youngster shot weakly into the goalkeeper's arms from eight yards.
Lincoln made Hearts pay for that after 73 minutes, when his powerful 25-yard drive entered the net, despite Gordon getting both hands to the ball.
Hearts: Gordon, Neilson, Pressley, Webster, Maybury, Hamill (Weir 77), Hartley, Kisnorbo, McAllister, Pereira (MacFarlane 51), McKenna (de Vries 66).
Subs Not Used: Moilanen, Wyness, Berra, Stewart.
Sent Off: Kisnorbo (48).
Booked: Kisnorbo, Neilson, Hartley.
Schalke 04: Rost, Pander, Bordon, Waldoch, Oude Kamphuis, Poulsen, Altintop (Kobiashvili 61), Lincoln, Asamoah (Varela 61), Ailton, Sand (Hanke 88).
Subs Not Used: Heimeroth, Klasener, Rodriguez, Vermant.
Booked: Rost. Goals: Lincoln 73.
Ref: Nikolai Ivanov (Russia)