Eastleigh have now only lost once in their last 11 league games, a run that leaves them just three points off the top seven.
The win gives Strevens his first win for the Spitfires since taking over the reigns on a permanent basis and the manager said he was proud of his side.
"It was a really good away performance," he said. "It's a tough place to come and play football.
"From the first minute the boys were really good. We worked on the gameplan through the week and they carried it out perfectly and for that, I'm really proud of them today.
"We thoroughly deserved the three points and it makes the journey worthwhile now. It's a long way and we're happy to put in a performance for the fans who travelled as well.
"Chesterfield next week will be another tough test, but one we're looking forward to. We'll have some down time and then get ready to go next week and hopefully put on another good performance at home."