Giroux, who also had an assist, signed a three-year, $19.5 million contract ($6.5 million average annual value) with Ottawa on July 13.
Alex DeBrincat and Shane Pinto also had a goal and an assist, and Mathieu Joseph had two assists for the Senators. Anton Forsberg made 21 saves.
Nick Suzuki had two assists in his preseason debut, and Sam Montembeault made 18 saves for the Canadiens, who have lost their first six preseason games (0-5-1).
DeBrincat gave Ottawa a 1-0 lead at 3:13 of the first period on the power play, a one-timer from Giroux for his third preseason goal.
Giroux extended it to 2-0 at 5:52 of the second period, tapping in a pass from DeBrincat.
Joel Armia cut it to 2-1 at 8:20, and David Savard scored 44 seconds later at 9:04 to tie it 2-2.
Tyler Motte scored his third goal of this preseason to give the Senators a 3-2 lead at 11:10, and Pinto restored the two-goal lead for the Senators with his fourth preseason goal at 18:53.
Cole Caufield scored on the power play to cut it to 4-3 at 14:57 of the third period, but Brady Tkachuk scored his first goal of the preseason 1:11 later at 16:08 to give Ottawa a 5-3 lead.
Arber Xhekaj had his wrist shot go off Joseph's hand at 16:36 for the 5-4 final.
