England World Cup winner Dawson ran the show as Ian McGeechan's side saw off a powerful Auckland outfit 17-13 at Eden Park.
And it completed a perfect five from five return following previous midweek wins against Taranaki, Wellington, Southland and Manawatu.
Dawson, together with the likes of Charlie Hodgson, hooker Gordon Bulloch and try-scorer Martyn Williams, must now wait to see if they have done enough in terms of gaining third Test selection for Saturday's All Blacks finale.
"It was a big win," said Dawson. "We've focussed really hard on this game since selection, it was our Test match, and for all the players who have been involved in the midweek sides, it has been a fitting end to a really good tour.
"A great team spirit has been built throughout the whole tour party."
Dawson made his first Lions start for more than three weeks, and he added: "I wanted to start, like every player in the tour party wants to start games. I want the number nine on my back, and I will support the squad wherever I am picked.
"But I don't want to be finishing my career in the next couple of years being known as someone who is on the bench, it's not how I work.
"It was a big game for me, and it was a big game for a lot of players out there.
"I don't go out there to prove points to anyone other than myself. I am a team player, and I hope my team-mates think I am a team player.
"I will only play well if the forwards play well, and they were pretty outstanding in the set-pieces.
"I am not even thinking about the weekend. Dwayne Peel has had an outstanding trip, and I will support him as much as I possibly can."
Irish fly-half Ronan O'Gara, who replaced an injured Hodgson after just 20 minutes and kicked three match-clinching penalties, could find himself in Test contention if Jonny Wilkinson is ruled out of Woodward's plans.
Wilkinson is struggling to overcome another 'stinger' injury in his shoulder/neck area.
"I knew I was in with a shout, because there is uncertainty over Jonny. I don't know whether he is playing in the Test match or not," said O'Gara.
"I missed two tackles in the first tour game against Bay of Plenty which was disappointing, and ever since then there were defensive question marks.
"But I just wanted to get back on the pitch and since then, it has gone well. I feel I have something to offer at Test level, but we will see.
"I analyse games in my own mind, and if I am happy with the way things have gone, then that is all you can do."