Alston, a defender who missed the last four games because of a pulled hamstring, scored his first goal of the season in the 68th minute. Bengtson added a goal in stoppage time.
New England (2-3-1) won for the second time its last three games and avenged a 4-0 loss at Houston in the opener. Houston (2-3-0) has lost three straight, allowed seven goals in that span.
New England goalkeeper Bobby Shuttleworth had to make just one save, that on a deflected ball in the 81st minute, for his second shutout of the season. The Dynamo did not have a scoring chance at all during the first 80 minutes other than five corner kicks, four during the first half by Boniek Garcia.
Nifty exchanges from Diago Kobayashi on the left side of the penalty box area to Teal Bunbury in the middle set up Alston's goal, a right-footed blast under the middle of the crossbar past goalkeeper Tally Hall.
Bengtson scored in the 91st minute on a run down the left wing with A.J. Soares assisting. New England was coached by assistant Tom Soehn as head coach Jay Heaps sat out a one-game suspension for arguing a referee's decision last week in a loss at San Jose.