Harvey's 14th-minute strike gave the home side the lead before Reid doubled Argyle's advantage nine minutes before the break. Nelson finished off the scoring with just seven minutes remaining to give Plymouth a resounding 3-0 win over their neighbours.
Portsmouth edged out Cambridge United despite Adam Webster's dismissal on the stroke of half time. Myles Storey set up Ryan Taylor for Pompey's opener before Chris Dunn's own goal doubled their advantage. Kwesi Appiah pulled one back for Cambridge with 20 minutes left on the clock but it wasn't enough to affect the result.
There was drama in the final minutes at Mansfield as Ryan Tafazolli's header looked to have won the game, but Danny Hylton equalised for Oxford United with 10 minutes remaining. Adam Murray stepped up just two minutes from time to score a dramatic winner for the home side as Mansfield ran out 2-1 winners.
Adam Chapman and Aaron O'Connor gave Newport County the away lead early on but Morecambe's Kevin Ellison pulled two goals back after 58 and 63 minutes before Paul Mullin's winner with just six minutes before full time.
Shrewsbury Town came from a goal down to beat Tranmere Rovers after Abdulai Bell-Baggie's opener was cancelled out by Andy Mangan. The match was then won by Mickey Demetriou in the fourth minute of added time.
Carlisle United thought they had earned a point against Wycombe Wanderers after Brad Potts cancelled out Aaron Pierrer's opening goal, but Paul Hayes and Peter Murphy both added to the scoresheet late on for the home side to earn a 3-1 win.
Elsewhere, Northampton Town scored a dramatic 90th-minute equaliser to share the spoils against York City. Marc Richards's goal sent the away fans into raptures after Anthony Straker's opening goal on 67 minutes.
Results in full: Burton Albion 2-1 Dagenham & Redbridge, Cheltenham 2-1 Accrington Stanley, Hartlepool United 0-2 Bury, Luton Town 0-1 AFC Wimbledon, Mansfield 2-1 Oxford United, Morecambe 3-2 Newport County, Plymouth Argyle 3-0 Exeter City, Portsmouth 2-1 Cambridge United, Shrewsbury Town 2-1 Tranmere Rovers, Southend United 2-0 Stevenage, Wycombe Wanderers 3-1 Carlisle, York City 1-1 Northampton