But with almost the last kick of the game Darius Henderson completed his first ever hat-trick and it was United's fans who left the ground celebrating.
"I don't want too many finishes like that - unless they all go my way," said Blackwell.
"When I was at Leeds United we were 3-0 down at Southampton and won 4-3 so it isn't the first time I've experienced this feeling.
"When City equalised I thought we had done everything right except win. Then Darius scored and the mood was transformed again.
"I think we deserved it. I still haven't been able to put out the same side in successive games this season, but our injury problems are easing and with a bit of luck it could happen next week."
Henderson's first goal on the half hour was controversial as a linesman was flagging for offside against a team-mate when his low shot beat Dean Gerken.
Referee Andrew Hall consulted his assistant and then awarded the goal, a decision which saw Lee Johnson booked for dissent after carrying City's protests too far.
A mistake by Jamie McCombe allowed Jamie Ward to set up Henderson for his second on 33 minutes, a close-range shot that went in off the crossbar.
City stepped up their game after the interval and replied when skipper Louis Carey headed home Paul Hartley's 53rd minute free-kick.
When Saborio shot home from 12 yards in a crowded box it seemed the home side's improvement would be rewarded.
But Henderson was allowed space to complete his treble with a shot from a narrow angle, leaving home boss Gary Johnson perplexed by his side's first home defeat.
"We have conceded a lot of late goals this season and this was a real gut-wrencher," he said.
"I'll be looking hard at the match video and the ones from our previous games to see if there is a common denominator about the late goals.
"Sheffield's first two were down to individual errors that you can't legislate for. I thought overall it was one of our better home displays.
"We now have another home game against Ipswich Town coming up and need to get our form back on track. The lads deserve credit for working really hard in the second half, but in the end it all counted for nothing."