Watch All Two Hours and 40 Minutes of the Titanic Sinking in Real Time

The animators made this video painfully accurate.  They also helpfully published a timeline of events that you can jump to in the video description as well:

0:30 - Iceberg spotted.
1:05 - Titanic collides with iceberg.
6:06 - The ship has stopped as damage inspections are carried out.
7:44 - Captain Smith orders engines to 'Half Ahead'.
19:41 - Titanic stops for the last time.
20:04 - Excess steam is vented.
38:08 - The Titanic begins taking on a 'starboard list'.
43:03 - Thomas Andrews estimates 1-2 hours before the ship sinks.
46:23 - The first distress calls are sent out.
48:38 - Lights of another ship are spotted on the horizon.
53:07 - Most lifeboats are prepared to evacuate passengers.
58:20 - Carpathia responds to Titanic's distress calls.
1:01:29 - Lifeboat 7 is launched.
1:05:03 - Lifeboat 5 is launched.
1:05:21 - The D-Deck gangway doors are opened.
1:06:04 - The telegraph operators begin using 'SOS'.
1:07:22 - Lifeboat 5 encounters lowering difficulties.
1:08:02 - Officer Boxhall launches the first distress rocket in an attempt to signal the ship on the horizon.
1:10:24 - The Carpathia confirms it is on it's way.
1:11:03 - Steam stops venting from the funnels.
1:13:20 - The starboard list is eliminated as Boiler Room 5 floods.
1:21:28 - Lifeboat 8 leaves.
1:28:22 - Suction pumps are activated.
1:31:33 - Lifeboat 6 is launched.
1:36:57 - Water is up to the Titanic's nameplate.
1:39:37 - Titanic begins listing to port.
1:41:43 - Lifeboat 16 is launched.
1:46:54 - Lifeboat 14 is launched.
1:51:18 - Lifeboat 14 is dropped 4 feet into the sea from its falls after they jammed.
1:51:42 - Lifeboat 12 is launched.
1:52:29 - Lifeboat 9 is launched.
1:58:53 - Lifeboat 11 is launched.
2:00:41 - Lifeboat 13 is launched.
2:05:21 - Lifeboat 13 is pushed aft by the discharging condenser, jamming it on the falls.