United, ANA, and Singapore Airlines has round-trip flights from Houston (IAH) to Singapore (SIN) for $621-$671 with a connection. Flights January to May. Departures on Tuesday, Wednesday, and Friday. Extended Weekends available.
Note: The routing on Singapore isn’t the best, since it connects in Manchester, England before heading to Singapore. You should be able to find faster routes on ANA / United.
Note: Some small OTAs on SkyScanner have this for $594. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.