The Patriots (2-0) managed just nine first downs after leading the NFL in points and yards last season.
"We have a long way to go," Brady said. "No one is coming to (our) rescue and save the day, so we've just got to fight through it."
In the second half, the teams had to deal with a torrential downpour that started at intermission.
On the 17 possessions in the first half, there were 11 punts, a lost fumble, one missed field goal, three field goals and a touchdown.
The officials didn't have a very good half, either, with one touchdown by each team and a lost fumble by New England's Julian Edelman being overturned by video review.
The only touchdown of the half came on the first series when Brady hit Dobson down the right side. It was the first reception for the second-round draft choice, who missed the opening 23-21 win over the Buffalo Bills with a hamstring injury.
"We were being pretty aggressive there in a short-yardage situation and (Dobson) slid behind him and I just gave it to him. He did all the work," Brady said. "I'm glad we got on the board early and got a lead. Playing ahead is always important, especially when you get (bad) weather conditions."
It marked the 50th straight game in which Brady has thrown a touchdown pass. Drew Brees, whose streak has ended, holds the NFL record of 54.
Brady completed 19 of 39 passes for 185 yards and one touchdown. Smith was 15 of 35 for 214 yards with no touchdowns and three interceptions.
With the rookie wide receivers still learning the offense, Brady relied on veteran Julian Edelman, who caught a career-high 13 passes one week after catching seven for two touchdowns.
Copyright 2013 by The Associated Press