Grosjean's crash right at the end of the session was a virtual carbon-copy of a similar accident in second practice on Thursday and his second in just one session on Saturday morning.
The Frenchman had earlier hit the inside barrier on turn-in to the chicane, puncturing a rear tyre.
Grosjean looked fast - he has been quicker than team-mate Kimi Raikkonen all weekend - but on the verge of being out of control.
There were two other heavy accidents during the session.
Ferrari's Felipe Massa had a big crash at Sainte Devote, hitting the outside barrier on the entry to the corner before smashing into the impact-absorbing barriers in the run-off area.
Ferrari said the crash was down to driver error - he locked the front wheels over a bump.
The team will need to change his gearbox, which will mean a five-place grid penalty if the car is repaired in time for qualifying. But that will be tight - with an hour to go, the team said that they were not expecting to have it finished until five or 10 minutes into the 20-minute first part of qualifying.
Massa's accident caused a brief stoppage, but no sooner had the session re-started than Adrian Sutil spun his Force India into the barriers at Massenet.
The officials allowed the session to continue while the German's car was winched out of the way.
Formula 1's magical Monaco moments
And in the initial minutes following the incident, Toro Rosso's Jean-Eric Vergne went straight on at Mirabeau and his team-mate Daniel Ricciardo and Mercedes' Lewis Hamilton both went straight on at the harbour-front chicane. None of the three incurred any damage.
The incident-packed final few minutes of the session meant that it provided an inconclusive picture of form ahead of qualifying, which starts at 1300 BST.
Rosberg, who has been fastest in all three practice sessions, looks in superb form, but Vettel was just 0.15secs down on the German at the entry to the second part of the Swimming Pool section, which marks the start of the final section of the circuit, before he had to abort that lap when he came across one of the Caterhams.
Alonso did manage to complete a lap and was a massive 0.908secs off the pace, but less happy with the set-up of the car than he had been on Thursday. Ferrari will make changes for qualifying.
Hamilton was fifth fastest ahead of Raikkonen and Red Bull's Mark Webber.
Force India's Paul di Resta was eighth from Williams's Pastor Maldonado, Sauber's Nico Hulkenberg and the McLarens of Sergio Perez and Jenson Button.
Practice three result:
1. Nico Rosberg - Mercedes - 1:14.378
2. Romain Grosjean - Lotus - 1:15.039
3. Sebastian Vettel - Red Bull - 1:15.261
4. Fernando Alonso - Ferrari - 1:15.286
5. Lewis Hamilton - Mercedes - 1:15.311
6. Kimi Raikkonen - Lotus - 1:15.380
7. Mark Webber - Red Bull - 1:15.550
8. Paul di Resta - Force India - 1:15.594
9. Pastor Maldonado - Williams - 1:15.861
10. Nico Hulkenberg - Sauber - 1:15.926
11. Sergio Perez - McLaren - 1:15.958
12. Jenson Button - McLaren - 1:15.976
13. Jean-Eric Vergne - Toro Rosso - 1:15.976
14. Daniel Ricciardo - Toro Rosso - 1:16.060
15. Adrian Sutil - Force India - 1:16.068
16. Felipe Massa - Ferrari - 1:16.105
17. Esteban Gutierrez - Sauber - 1:16.427
18. Valtteri Bottas - Williams - 1:16.933
19. Charles Pic - Caterham - 1:17.902
20. Giedo van der Garde - Caterham - 1:18.102
21. Jules Bianchi - Marussia - 1:18.706
22. Max Chilton - Marussia - 1:19.228
Monaco Grand Prix, day two
Saturday, 25 May: Qualifying: BBC Radio 5 live 13:00 BST, live text commentary on the BBC Sport website. TV highlights 17:35 BST, BBC One
Monaco Grand Prix, day three
Sunday, 26 May: Race: Coverage on BBC Radio 5 live from 13:00 BST and live text commentary on the BBC Sport website from 12:00. TV highlights 17:35 BST, BBC One
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