Goals from Lewis Finney, Alex Fair and Liam Hendy scored the goals to force the game into a replay which will take place next Saturday at Culver Road.
Finney opened the scoring for the Lancers on 21 minutes from the penalty spot.
Fair then put the visitors 2-0 one with a superb strike on the edge of the box which nestled into the top corner.
SCR pulled a goal back on 51 minutes when Brendan Murphy-McVey spotted Matt Evans in the Lancing goal off his line and superbly lobbed him from 25 yards.
Just as Lancing thought they had seen out the game, the Commoners equalised in the third minute of stoppage time as Matt Farrell got on the end of a free-kick to stroke home and send the game into extra time.
The hosts then took the lead in the eighth minute of the first half of stoppage time as Farell converted from the penalty spot.
The Lancers managed to pull the game even again on 109 minutes when Hendy headed home to ensure the replay.
After the match the Lancing manager talked about his experience of going through the highs and lows that were encapsulated in the match.
He said: “Football is a game of emotions and through the 90 minutes both teams will go through different emotions.
“The first half was arguably our best half of the season.
“In hindsight we probably should have gone for it a little bit more as on the balance of play I thought we were worth more than the two goal lead. It was that dominant.
“In the second half I was expecting a reaction from Sutton Common Rovers.
“They’re a decent side with a lot of experience and know how and they had nothing to lose and to be fair to them they came out strong and gave it a good go.
“You have to respect that there are not many sides that are going to put large spells of possession together the way we do and dominate that way but they found ways to get back into the game.
“Conceding late on is obviously disappointing but this is football and these things can happen maybe. (It’s) something we have to look at in future games and possibly be more game smart.
“Credit to our boys after they took the lead and went 3-2 up we could have thrown the towel in but the boys stuck to their principles worked the ball well and equalised through Liam Hendy who I thought he was excellent on the day and deserved his goal.
“From then on if there was going to be a winner it was only going to come from us and to be honest I really felt we should have got the winner we got into really good positions we just lacked the final pass or finish.”
The Lancers return to league action on Saturday where they will host fourth-placed Horley Town.
Lancing: Evans, Beresford (Honore 98), Juwara (Coupar 57), Williamson, Sharman, Hendy, Rhodes, Woolven, Fair (Mitchell-Philips 87), Caplin, Finney
Unused: Hewens, Altendorff, Seymour