Fresh from his hat-trick heroics in the 3-2 win over Peterborough, Eastwood netted after 72 minutes of Saturday's clash at Home Park as the Sky Blues claimed their first away win since the end of September.
While back-to-back Championship victories have propelled Chris Coleman's men clear of the drop zone, a run of five successive defeats has left Argyle stuck in the mire.
With both sides toiling at the wrong end of the Championship table, it was of little surprise they played out a low-key opening at Home Park.
Argyle's Jamie Mackie created the first half-chance after 23 minutes but his 12-yard effort was blocked by the imposing figure of Leon Barnett.
Chris Clark was next to try his luck for the home side just after the half-hour mark before the lively Eastwood rifled wide from 25 yards during a rare Coventry attack.
Alan Judge's weak free-kick drew a comfortable save from Keiren Westwood but it was the visitors who were unfortunate not to go in ahead at the half-time interval as Coleman's side spurned three chances in the space of as many minutes.
Michael McIndoe's close-range shot first struck Kari Arnason and Barnett failed to hit the target with the rebound. Leon Best then headed wide from McIndoe's left-footed free-kick with the goal seemingly at his mercy.
Westwood had to be alert eight minutes after the restart to parry Carl Fletcher's 20-yard strike.
The Pilgrims again went close to breaking the deadlock three minutes later as Rory Fallon rose well to meet another Judge set-piece but the New Zealand international planted his close-range header over.
Fallon, who scored the decisive goal to help the All Whites qualify for next year's World Cup, diverted another close-range header off target just after the hour mark from Shane Lowry's centre.
Judge continued to prove a threat from set-pieces but the home side were left to rue their profligacy as Eastwood broke the deadlock with 18 minutes remaining.
McIndoe's neat pass allowed David Bell to send an inviting cross in from the right wing and Eastwood made no mistake from six yards, heading high beyond Romain Larrieu.
Fallon had a goal-bound effort blocked by Elliott Ward as Argyle battled to get back on level terms immediately before Bell hacked Lowry's header clear from a Craig Noone cross.
Westwood held his nerve to deny Fallon late on as Coventry clung on for the three points.