The Scot joined the Chairboys this summer from Partick Thistle and halted his new side's mini-slump of four games without a victory as his header just after half an hour proved to be the winner.
But with 15 minutes of the first half left Craig glanced Max Kretzschmar's corner home to put Wycombe back in front.
The visitors almost pulled level again before half-time but John White saw his bullet header cannon back off the crossbar.
Eastwood forced Wycombe goalkeeper Matt Ingram into some fine saves after the break before Anthony Straker crashed an effort against the bar immediately after the shotstopper had denied him from point-blank range, but Southend could not find an equaliser.
- Sports & Recreation
- Freddy Eastwood
- Partick Thistle
- Ryan Leonard