Edinburgh number eight Allister Hogg came through 80 minutes unscathed ahead of next weekend's Six Nations opener with England.
Hogg was attempting to prove his fitness to Scotland boss Frank Hadden ahead of the Calcutta Cup clash at Twickenham having missed much of the season, including the November 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 Conor McPhillips was touching down with Paul Warwick converting from touch.
Second bottom of the Magners League, 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 Rob Dewey who sold a lovely dummy to open up the line.
It suddenly became all Edinburgh and after Ben Cairns had sent Simon Webster to the Connacht corner the visitors over-threw at the line-out to Ally Strokosch who battered over. With Hodge converting both, Edinburgh led 14-7 after 20 minutes.
Warwick pulled back a penalty from the re-start but Edinburgh returned to the attack. Their third try arrived when Webster, who seemed back to his best, shot though centre field 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 shot through a static Edinburgh defence, so Edinburgh 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, John 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 grabbing a try through Dan Riordan with Warwick converting.
In a tight finish Webster had a second try and Phil Godman kicked a penalty for Edinburgh while David 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.
The scorers:
For Edinburgh:
Tries: Dewey 2, Strokosch, Dewey, Senio, Webster
Cons: Hodge 5
Pens: Hodge 2, Godman
For Connacht:
Tries: McPhillips 2, Riordan, Gannon
Cons: Warwick 4
Pens: Warwick 1
Yellow card: Riordan (Connacht, 48 min)
The teams:
Edinburgh: 15 Andrew Easson, 14 Matt Dey, 13 Ben Cairns, 12 Rob Dewey, 11 Simon Webster, 10 Duncan Hodge (c), 9 John Senio, 8 Allister Hogg, 7 Ross Rennie, 6 Alasdair Strokosch, 5 Scott Murray, 4 Matt Mustchin, 3 Geoff Cross, 2 Steven Lawrie, 1 Allan Jacobsen.
Replacements: 16 Andrew Kelly, 17 David Young, 18 Chris Bentley, 19 Alan MacDonald, 20 Greig Laidlaw, 21 Phil Godman, 22 Lucio Lopez Fleming.
Connacht: 15 Daniel Riordan, 14 John Hearty, 13 Gavin Williams, 12 Mark McHugh, 11 Conor McPhillips, 10 Paul Warwick, 9 Conor O'Loughlin, 8 Colm Rigney, 7 Ray Ofisa, 6 M Lacey, 5 Andrew Farley, 4 David Gannon, 3 Stephen Knoop, 2 John Fogarty (c),1 Brett Wilkinson.
Replacements: 16 Adrian Flavin, 17 Ray Hogan, 18 Michael Swift, 19 Brendon O'Connor, 20 Chris Keane, 21 Peter Durcan, 22 David Slemen.
Referee: Neil Ballard (Wales)
Touch judges: Andy Ireland (Scotland), David Anderson (Scotland)
Assessor: Jim Fleming