An ignition system for a multi-burner heat exchanger assembly, a furnace, and a method using same are disclosed. The assembly may include a plurality of adjacent heat exchanger tubes, with a burner associated with each tube. All the burners may be lit with a single igniter and no source of secondary air. To do so, each of the burners may be provided so as to generate a swirling exit flow of combustion gases. One or more carryover tubes may also be connected between adjacent pairs of heat exchanger tubes or adjacent pairs of burners. The swirling flow generated by the burners causes hot combustion gases to move through the carryover tubes to thus carry the flame from one burner to the next. Not only can a single igniter be used, but a single flame sensor as well, while at the same time reducing nitrogen oxide emissions.