An Edgaras Jankauskas double was enough to see Hearts comfortably through to
the third round of the CIS Insurance Cup against Queen's Park at Hampden.
Jankauskas celebrates the first of his goals
Lithuanian international Jankauskas opened the scoring with a tap-in after David Crawford had parried a Stephen Simmons effort.
He found the net again a minute before the break.
Jamie McAllister was the provider and Jankauskas could not miss with a close-range shot at the back post.
The Glasgow part-timers had looked lively for a period, with Andy McGinty
causing a panic in the Hearts defence.
But the biggest worry for Burley came with the loss of both Michal Pospisil
and Neil MacFarlane to injury in the first half.
Deividas Cesnauskas could have put the game beyond Queen's Park after the
interval when he teed up a long-range shot only to send the effort fizzing just
past the upright.
Queen's showed they had not entirely given up hope of a fightback when Mark
Ferry burst forward and bulleted a header narrowly wide of the target.
Lee Wallace could have made the scoreline more flattering for Hearts with a
couple of minutes to go only to send the effort across the face of goal and
trundling harmlessly wide.