Dutch striker Dost got his maiden Champions League goal a minute after the restart and in-form Kruse added another with a glancing header in the 57th minute with keeper Diego Benaglio saving a PSV penalty in stoppage time.
The result lifts Wolfsburg, who have also gone 27 home matches in the Bundesliga without defeat, to six points, two ahead of Manchester United and CSKA Moscow, who drew 1-1 in Russia.
PSV have failed to win away against German opposition for 15 consecutive games in a run stretching back to 1977 and are bottom on three points.
"We were clearly the better team and deserved to win," Wolfsburg's Julian Draxler told reporters. "We have now taken a big step. You have to win your home games and that is what we are doing at the moment. We can now build on these six points."
Wolfsburg, who ended a four-match winless run in the Bundesliga by beating Hoffenheim 4-2 on Saturday, set a frenzied early pace and had four attempts on goal in the first four minutes.
The visitors, with top scorer Luuk De Jong back fit, gradually managed to keep more possession and took some of the sting out of Wolfsburg.
Luiz Gustavo fired over the bar with the Germans' best chance of the first half just after half an hour while PSV responded with Adam Maher, left completely unmarked in the box, rising high to head narrowly wide three minutes before the break.
Wolfsburg were stronger after the restart and the 26-year-old Dost, who has scored six times in the league this season, tapped in on the rebound after keeper Jeroen Zoet had saved a shot from Josuha Guilavogui for his maiden goal in the competition.
Germany international Kruse's glancing header gave them a two-goal cushion as their early pressure in the second half paid off.
PSV never found a way back into the game even after coach Phillip Cocu brought on another striker in Juergen Locadia, who had his stoppage time spot kick saved.
(Reporting by Karolos Grohmann; editing by Toby Davis)
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