Dominic Cork saluted his opening batsmen after they bailed Hampshire out of trouble at the Rose Bowl.
A first-wicket stand of 171 settled the nerves of the side who knew they had to bat out the entire day to avoid defeat in their Championship opener.
Adams (105) and Dawson (70) played with cool heads to see the team through to lunch with the rest of the batting line-up digging in to ensure there was no collapse.
And Durham – minus the injured Steve Harmison – were never able to exert enough pressure on the home side to secure a victory that they will feel they deserved after dominating the majority of the game.
Cork said: ‘We all know everything about Jimmy Adams.
‘He is a superb opening batsman and together with Liam, it was a match-saving partnership.
‘You cannot go out there and block for six hours.
‘You’ve got to be positive and they did that.
‘It’s a loss to lose Michael Carberry but Liam can bat and do it for long periods of time. I was very pleased to see Liam do well.
‘We’ve shown that we can fight and keep ourselves in a game. But those two did very well for us.
‘It was a test because I don’t think we played as well as we should have done.
‘We were dominated for the first two-and-a-half days against a well-equipped side.
‘We talked about hitting the ground running this season and for those first two days, it didn’t look like that was the case.
‘But we had to show a bit of a rearguard action and the guys did well.
‘It gives us a bit of momentum now going into the game with Nottinghamshire at Trent Bridge.
‘Hopefully, we can start a bit better than we did in this game.’
While Cork was unable to bowl in the Durham second innings because of a groin injury, he is confident he will recover in time to lead the side for their next Championship clash at Nottinghamshire on Thursday.
He said: ‘I’m fine. It was just a bit of cramp in the left groin so hopefully it should be okay.’
Team-mate Simon Jones will not be included, however, after he suffered a more serious groin strain.
Cork said: ‘Simon Jones is a little bit worse and he looks like he could be out for 10 days.
‘But it gives opportunities to the likes of Chris Wood and David Griffiths to come into the side.’