A record Warriors crowd of 8,855 watched as Gregor Townsend's team claimed just their second bonus-point win of the campaign to jump above Ulster and Munster into second.
Peter Murchie's double and scores from Ruaridh Jackson, Mark Bennett and Rob Harley, as well as 12 points from kicker Finn Russell, clinched Glasgow's sixth successive victory.
They now move to 69 points, five behind leaders Leinster with two games remaining.
Willem Nel and Matt Scott crossed over for Edinburgh but they looked well out of the contest until Tim Visser crossed over twice in the last three minutes.
Skipper Greg Laidlaw contributed 14 points with his boot, but it was not enough for a side who continue to disappoint after just two wins in their last 10 fixtures, although they did land two bonus points for their efforts.
As well as Pro12 points, there was also the 1872 Cup at stake for both sides.
Warriors had held the edge in the aggregate scores following their 20-16 first-leg win at Murrayfield on Boxing Day, but were never in danger of seeing their lead overturned.
The match was the first since Jackson announced he is heading to Wasps this summer and he was afforded a warm cheer as he ran out for kick-off.
Scotland colleague Laidlaw was back for Alan Solomons' team after he was given a six-week break ahead of the Dark Blues' June tour of North America, Argentina and South Africa.
With so much at stake for the hosts, Russell's early penalty and Murchie's eighth-minute touchdown were exactly the start they were looking for.
The traffic was moving in one direction only as Glasgow remained patient while working through the phases before finding Murchie, who squeezed over in the corner for the opening try.
Russell failed with the conversion but made amends with another penalty to put an ominous slant on the scoreline.
Edinburgh had barely managed to cross halfway in the opening stages, but an inspired Laidlaw surge opened up a chink in the Warriors defence. The Scotland vice-captain was clobbered by Russell just as he looked to score, but from the breakdown Nel rolled round the ruck and dived over to give his side their first points on the quarter-hour mark.
Laidlaw excelled again with the conversion from out wide, but there was relief for Glasgow as the TMO ruled Bennett's last-ditch tackle had put Andries Strauss into touch as he dived over.
Another Laidlaw kick briefly took the visitors to within a point of their rivals.
However, Edinburgh switched off from the restart to concede crucial territory and Jackson punished the capital club as he sold their defence a dummy to touch down after 23 minutes, although Russell missed the bonus points.
The build-up to the try was marred by lock Izak van der Westhuizen's neck-high tackle on Bennett and he was sentenced to a 10-minute stint in the sin-bin.
But despite his side's numerical disadvantage, Laidlaw closed the gap back to three with another penalty.
Townsend's men did not hang about though, as they raced up field for one last attack before the break. It proved a wise ploy and from a line-out, scrum-half Chris Cusiter found Bennett offering the perfect angle to crash home. Russell then converted to hand his side a 10-point half-time lead.
Edinburgh had Van der Westhuizen back by the start of the second period but again found themselves a man down when flanker Mike Coman was yellow carded as he killed the ball one time too many for French ref Mathieu Raynal's liking.
And the holes his absence left were clear to see when Murchie jinked his way in for the crucial fourth score after 49 minutes, with Russell converting.
Scott barged his way in from close range to hand Edinburgh hope after 58 minutes, with Laidlaw's conversion closing the gap to 10.
Substitute Moray Low was denied a try as Niko Matawalu chucked him a forward pass. but Harley benefited from Richie Vernon's instinctive off-load to career over for what turned out to be the match-winner four minutes from the end, with Russell again putting over the extras.
Visser darted in for a pair of last-ditch tries, both converted by Laidlaw, but Glasgow had already done enough for the win.