Rob Dewey grabbed a brace for Edinburgh
Edinburgh: (24) 49
Tries: Dewey 2, Strokosch, Senio, Webster 2
Pen: Hodge 2, Godman
Cons: Hodge 5
Connacht: (17) 31
Tries: McPhillips 2, Riordan, Gannon
Cons: Warwick 3, Slemen
Edinburgh came out on top against second-bottom Connacht after the Irish side got off to a flying start in their Magners League match on Friday.
Connacht winger Conor McPhilips went over after six minutes before a Rob Dewey double and an Ally Strokosch try sparked the home side into life.
Connacht scored three tries through McPhillips, Dan Riordan and David Gannon to get back into the match.
But a Simon Webster brace and one from John Senio ended their brave fightback.
Edinburgh's Ally Hogg came through 80 minutes unscathed ahead of Scotland's Six Nations opener with England.
Hogg was attempting to prove his fitness to national boss Frank Hadden ahead of the Calcutta Cup clash at Twickenham having missed much of the season, including the autumn internationals, before making an aborted comeback.
Hogg, who turned 24 last Saturday, was looking to add to his 24 caps but it was Ireland's Cinderella side who took the attention early on.
Their sharpness was rewarded in the sixth minute.
Veteran home stand-off Duncan Hodge dropped a pass from a scrum, visiting scrum-half Conor O'Loughlin pounced on it and several pairs of hands later winger McPhillips was touching down with Warwick converting from touch.
Connacht continued to look lively until a Scott Murray burst suddenly sparked life into the home side.
The vital try to get back into it was scored by another comeback man Dewey who sold a lovely dummy to open up the line.
It suddenly became all Edinburgh and after Ben Cairns had sent Webster to the Connacht corner the visitors over-threw at the line out to Strokosch and he battered over.
With Hodge converting both, Edinburgh led 14-7 after 20 minutes.
Warwick pulled back a penalty from the restart but Edinburgh returned to the attack.
Their third try arrived when Webster, who seemed back to his best, shot through before unloading to Dewey who touched down by the posts with Hodge converting.
However, Connacht got back into it with a second McPhillips try converted by Warwick who had beaten a static Edinburgh defence, so the hosts were thankful for a last-minute penalty from Hodge that let them turn 24-14 ahead.
Within 90 seconds of the restart Edinburgh had the bonus point, Senio getting over from close in with Hodge converting and soon adding a penalty.
In the 50th minute Webster added a spectacular try, running back a clearing kick through despairing tackles.
Hodge converted but Connacht still had life and grabbed a try through Riordan with Warwick converting.
In a tight finish Webster had a second try and Phil Godman kicked a penalty for Edinburgh while Gannon scored Connacht's fourth try converted by David Slemen.
While Hogg came through only his seventh Magners League game of the season unscathed, Webster seemed ready for Twickenham.
Edinburgh: Andrew Easson; Matt Dey, Ben Cairns, Rob Dewey, Simon Webster, Duncan Hodge (c), John Senio; Allan Jacobsen, Steven Lawrie, Geoff Cross, Matt Mustchin, Scott Murray, Alasdair Strokosch, Ross Rennie, Allister Hogg.
Replacements: Andrew Kelly, David Young, Chris Bentley, Alan MacDonald, Greig Laidlaw, Phil Godman, Lucio Lopez Fleming.
Connacht: D Riordan; J Hearty, G Williams, M McHugh, C McPhilips; P Warwick, C O'Loughlin; B Wilkinson, J Fogarty (c), S Knoop; D Gannon, A Farley; M Lacey, R Ofisa, C Rigney.
Replacements: A Flavin, R Hogan, M Swift, B O'Connor, C Keane, P Durcan, D Slemen.