Groves then came to the rescue to force the ball out of play after a misunderstanding between keeper Tommy Evans and Wayne Graves, while Yeovil's Adam Stansfield forced Evans to a good stop after nine minutes, when he capitalised on a flick on by Hugo Rodrigues.
Play was rather untidy, but Scunthorpe found themselves ahead after 26 minutes and Groves was again involved when he headed down for MacLean to volley home a right foot drive beating Chris Weale at his right-hand post.
There was a lively spell just prior to the interval with Steve Torpey forcing Weale to fingertip a header over the bar and then he headed over following a Kevin Sharp corner.
However, in added time before the break Scunthorpe struck a second time, Sharp's corner was headed home off the underside of the bar by Darren Holloway, who is on loan from Wimbledon to mark a solid debut.
On the hour, Scunthorpe grabbed a third goal which sealed the victory.
Winger Cleveland Taylor, who was a constant threat throughout, got the ball in from the right and MacLean stabbed the ball home at the second attempt. Little was seen of Yeovil's attack as Scunthorpe's rearguard - marshalled well by stand-in skipper Nathan Stanton - worked tremendously hard.
Substitute Lee Elam fired straight at Evans while Andy Lindegaard fired over when he had an opportunity but those were just a few flickering attempts from the visiting attack which lacked imagination.