Two tries from England wing Mark Cueto gave Sale Sharks an seven-point advantage after the first leg of this European Challenge Cup semi-final.
Cueto, who spent ten minutes in the sin bin, went over twice in the final eight minutes as the Zurich Premiership side put one foot into the final with victory at Connacht.
But a push-over try from flanker Matt Lacey in the sixth minute of injury time handed the Irish province some hope for the return at Edgeley Park in three weeks' time.
Lacey was shoved over from a lineout yards from the Sharks try line in a similar move to that which saw skipper Andrew Farley give Connacht the lead in the first half moments after Cueto had been shown a yellow card for deliberately killing the ball.
Sharks outside-half Mike Hercus, a late replacement for the injured Charlie Hodgson, had slotted a drop goal and penalty to give the visitors an early lead only to squander his next five attempts at goal.
Things got worse for Sale and Hercus when opposite number Eric Elwood slotted over a drop goal early in the second half to open an 11-6 lead.
Both sides were reduced to 14 men when opposing props Ray Hogan and Barry Stewart, who had only been on the field a matter of minutes, were sent to the sin bin for fighting.
The cards appeared to effect Connacht more and eight minutes later the Sale scrum rumbled over the try line for Frenchman Sebastien Chabal to touch down.
Chabal then had a hand in both of Cueto's tries, both from scrums in identical positions, as Sale aimed to rack up a commanding lead for the second leg.
They looked to have achieved that until Lacey typified Connacht's determination with a late effort that kept the tie well and truly alive.