Garmin completed the 33.2km route in north Italy in a time of 37 minutes and four seconds, five seconds faster than surprise runners-up Katusha.
The BMC team of former race leader Taylor Phinney could only post the 10th best time, 31 seconds off the pace, meaning Phinney dropped to fifth in the GC.
Navardauskas now tops the overall standings ahead of team-mates Tyler Farrar, Robbie Hunter and Ryder Hesjedal.
Twenty-four-year-old Navardauskas started the day 18 seconds down on Phinney in the overall standings but took the maglia rosa after his Danish team-mate, Alex Rasmussen, failed to keep up with Garmin's blistering pace during the collective race against the clock.
Rasmussen was 13 seconds behind Phinney and third place in the GC overnight, but finished outside his American team's strongest five riders on the cobbled streets of Verona.
"It’s fantastic, we really love the team time trial here at Garmin, and to take the pink jersey makes it even better," said sprinter Farrar, who trails team-mate Navardauskas by 10 seconds in the overall standings.
It was an eventful day for BMC's Phinney, who started the TTT despite injuring himself badly in the pile-up which marred the finale of Monday's stage three in the Danish town of Horsens.
Riding with four stitches and his right ankle heavily strapped, 21-year-old Phinney almost crashed again on Wednesday after he rode onto grass verge beside the road. The error cost his BMC team a lot of time as they were forced to regroup just after the half-way point of the largely flat route.
Phinney is now 13 seconds off the summit in the overall standings, with Italian Manuele Boaro six seconds behind in sixth after his Saxo Bank team set the third fastest time of the day.
Another team to suffer was Mark Cavendish's Sky outfit, who could only set the ninth best time despite being tipped as one of the favourites. Welshman Geraint Thomas, second in the GC overnight, was seen by many as a likely candidate for the pink jersey, but Team Sky crossed the line 30 seconds slower than Garmin.
Thomas drops to seventh in the GC, 21 seconds behind Navardauskas.
Katusha's strong second place will be a boost for Spaniard Joaquim Rodriguez, one of the race favourites, who took another 29 seconds off defending champion Michele Scarponi, whose Lampre team set only the 12th best time, 34 seconds behind Garmin.
Rodriguez is now 10th in the GC, just 30 seconds down after an opening four stages which many had predicted would see the climbing specialist lose much more time.
"My team-mates were spectacular today - we couldn't have gone a second faster," said Rodriguez. "I'm very happy because we gained seconds over all the other favourites and this gives me strong motivations and a great morale."
The Giro continues on Thursday with the 209km flat stage five from Modena to Fano, which should see Cavendish renew his sprinting rivalry with former team-mate Matthew Goss (Orica GreenEdge), winner of stage three.
1. Garmin-Barracuda 37:04, 2. Katusha +5, 3. Saxo Bank +22, 4. Astana +22, 5. Omega Pharma-QuickStep +24, 6. Orica GreenEdge +25, 7. Liquigas +26, 8. RadioShack +28, 9. Sky +30, 10. BMC +31
1. Ramunas Navardauskas (Garmin), 2. Tyler Farrar (Garmin) +10, 3. Robbie Hunter (Garmin) +10, 4. Ryder Hesjedal (Garmin) +11, 5. Taylor Phinney (BMC) +13, 6. Manuele Boaro (Saxo Bank) +19, 7. Geraint Thomas (Sky) +21, 8. Sebastien Rosseler (Garmin) +25, 9. Christian Vande Velde (Garmin) +26, 10. Joaquim Rodriguez (Katusha) +30