Smith's side in fact lost ground on 11th-placed Ross County in the Clydesdale Bank Premier League table, but there were plenty of positives to take out of a game where they could have arguably walked away with all three points.
John Baird opened the scoring on seven minutes, finishing a slick, largely one-touch passing move with a cool finish.
"The first goal was a great goal, with the passing between the midfield and the strikers to get the finish," Smith said.
"And I'm delighted for John Baird to get the first goal because he works so hard and he deserves all the credit. I thought it was an excellent away performance. It showed the effort and commitment we've put in the last few games, but with also a lot of quality as well.
"We were positive; we started with a lot of forward-thinking players. We were under a bit of pressure towards the end, but we didn't just create chances in the first half, we created them in the second half as well."
Hibs manager Pat Fenlon branded his side's performance "not good enough" as his side lacked urgency for large stretches of the match.
Leigh Griffiths equalised for the hosts with a second-half free-kick, but it was the visitors who created more chances over the course of the 90 minutes. The performance was certainly at odds with those Hibs produced in the two games against Celtic and Hearts before the winter break.
Fenlon said: "We just looked lethargic. It took us too long, we never started the game. Dundee started well and I suppose we only got going in the second half
"We had started really well in the last two games and we just didn't have the focus. We didn't start on the front foot, the first pass was sloppy and it went from there. We were too loose and didn't have the right tempo. We didn't play well and we know that."