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The Robins had play-off ambitions of their own until fairly recently, although five defeats from the last six games have sent their season into an alarming slump.
Southend, by comparison, have now lost only once in 17 league and cup games since the turn of the year.
Despite all this, Cheltenham could have gone ahead as early as the 10th minute when lively striker Steven Gillespie was brought down on the edge of the box by Spencer Prior. Grant McCann fired the free-kick at goal but right-back Duncan Jupp was in place to head it off the line.
Southend survived that scare and took the lead with their first real chance of the game on 16 minutes.
Leading scorer Eastwood collected a loose ball inside the Cheltenham half and sprinted forward. His pass found Gray on the edge of the area and the former Wimbledon striker rolled off his marker before beating goalkeeper Shane Higgs with a low drive.
Higgs saved well from a Mark Bentley header but, at the other end, Southend goalkeeper Darryl Flahavan dived to hold a spectacular bicycle kick from Gillespie.
Cheltenham had taken the game to their visitors in the hope of creating an equaliser, but they were hit by another sucker punch in the seconds leading up to half-time.
Again it was Eastwood who supplied an accurate through ball and Gray held off the attentions of Gavin Caines before drilling another accurate shot beyond Higgs.
The home fans would have expected an 'up and at 'em' charge at the start of the second half but it never materialised and Cheltenham surrendered with a meek second 45 minutes.
Southend controlled the game with some confident passing and incisive attacking play. They added a deserved third goal on 67 minutes when Gray turned provider, sending Eastwood away with a pass for the leading scorer to shoot past Higgs from the edge of the box.
Only in the closing minutes did Cheltenham threaten with Flahavan having to make flying saves from McCann and substitute Michael Taylor. By then, however, the contest was long over.