The liberals helped balance their books like most politicians balance their books, by cheating.
They made changes to employment insurance requirements which resulted in fewer eligible people. While not necessarily a bad thing based on circumstances, they failed to then adjust the EI payment rates to reflect the new number and instead kept it artificially high to collect more money than following the federal formula would normally allow.
They also made significant cuts to the transfer payments to the provinces, offloading Federal expenses to the various provincial governments. In your household anology, this would be like a slumlord putting in new flooring and an in ground pool at his house while letting all his tenant buildings going to ruins and pointing at his beautiful house to prove how great a real estate mogul he is.
The also greatly benefited by the implementation of the GST under the previous government, the abolishment of which was a major party platform that the Liberals ran on. Surprising no one with a functioning brain cell, the Liberals decided NOT to get rid of the GST once in power.
In general, neither the Conservatives or Liberals have been great at putting forward useful budgets that actually work, the liberals were just a bit better at making theirs look good on paper.