Blues took the lead through Freddy Eastwood before two goals from Robert Earnshaw and a single Dickson Etuhu strike put the visitors on course for their first away league win of the season.
But Steve Hammell got Blues back into the game before Gower slammed home the equaliser to earn the Shrimpers a standing ovation at the final whistle.
Norwich were quick out of the blocks with Andy Hughes and Lee Croft firing wide before Southend took the lead against the run of play.
Adam Barrett spotted Eastwood well placed and pumped a pinpoint forward ball to him.
Eastwood controlled it sublimely before losing central defender Jason Shackell and rifling the ball past City keeper Paul Gallacher for his fifth goal of the season after nine minutes.
Both sides traded blows as they searched for goals but did not enjoy any success until the 36th minute when the Canaries scored their first goal away from Carrow Road.
Earnshaw read Hughes' centre from the right perfectly to sneak in at the far post and head goalwards from close range.
Home goalkeeper Darryl Flahavan parried the shot onto his right post but the ball bounced out to Earnshaw who stabbed home his fifth goal of the season.
Three minutes later the Shrimpers were 2-1 down, with dangerman Earnshaw getting his second.
Colin's ball from the right caused chaos in the Southend 18-yard box with two shots being blocked before a clearance fell to Earnshaw, whose shot somehow found a way through the forest of bodies between him and the goal.
Southend found themselves 3-1 down after 47 minutes when Croft was left unmarked on the right and fired over an inviting cross for Etuhu to head home his first league goal for Norwich.
The hosts responded in style with Kevin Maher, Hammell and Luke Guttridge being denied by a combination of Gallacher and Gary Doherty.
Shrimpers boss Steve Tilson made a triple substitution, throwing Matt Harrold, Gary Hooper and Lewis Hunt on to try and force the issue.
Tilson was rewarded after 69 minutes when Eastwood touched a free-kick to Hammell and he curled a right-foot shot into the top left-hand corner of Gallacher's goal.
Southend pressed for an equaliser and pegged the Canaries back as Maher, Eastwood and Gower all went close.
And they finally netted a deserved leveller two minutes into stoppage-time after Gallacher could only push away an Eastwood shot into Gower's path, and the winger made no mistake from 12 yards.