Theo Walcott gave the Gunners the lead at the end of an awkward first half, but the visitors were overwhelmed after the restart as Arsenal ultimately ended their dream run in comfortable fashion.
Lincoln's victory over Burnley in the last round saw them become the first non-league team to reach the quarter-finals of the FA Cup since 1914, and Arsene Wenger named close to a full-strength side in an attempt to avoid becoming the latest team toppled by the Imps.
Despite such a strong starting lineup, the Gunners struggled to settle into their rhythm in the opening exchanges as Lincoln made a flying start - enjoying 62% of the possession in the opening six minutes.
Arsenal did soon begin to see the lion's share of the ball, but clear chances were relatively few and far between for the hosts considering they sit 88 places above Lincoln in the English football pyramid.
Aaron Ramsey had the first notable sight of goal for the Gunners when he was teed up just inside the area, but he failed to hit the target when looking to feed his shot into the bottom corner.
The hosts came even closer shortly afterwards when Walcott struck a crisp first-time volley towards the bottom corner from the edge of the area that Paul Farman did well to turn against the post.
It was a largely frustrating half for the Premier League outfit, though, and they were forced into an early change too as Alex Oxlade-Chamberlain limped off with an apparent hamstring injury, being replaced by Mesut Ozil.
Lincoln had a glorious chance to take a famous lead moments after that change when Nathan Arnold raced down the right flank before cutting inside past Koscielny, but his eventual effort was tipped past the post by Petr Cech.
It proved to be the Imps' only real opportunity of the night, but they continued to hold their own in the first half despite Walcott, Ramsey and Ozil all coming close.
The breakthrough finally arrived in the first minute of stoppage time at the end of the opening period, though, and there was an element of luck about it as Walcott's shot took a deflection off Samuel Habergham which sent it into the bottom corner.
Lincoln would have gone into the break feeling unfortunate to be behind, but Arsenal's superior quality began to tell after the restart and only a smart low stop from Farman kept the deficit at one before Kieran Gibbs headed another chance over the top seconds later.
It was merely delaying the inevitable, though, and Lincoln's resistance was broken again in the 53rd minute when Hector Bellerin exchanged passes with Sanchez before pulling the ball back for Giroud to sweep home.
Bellerin should have got his own name on the scoresheet four minutes later when he curled an effort wide of the target from a good position, but Arsenal's third arrived soon enough when Luke Waterfall could only turn Gibbs's low cross into his own net.
Lincoln continued to tire as Arsenal took complete control of the contest, and it soon became a question of how many the Gunners would score as they queued up to have a go at the visitors' goal.
A fourth arrived with just under 20 minutes remaining as Sanchez got in on the act, eluding a wild challenge from Bradley Wood before effortlessly stroking the ball into the bottom corner from the edge of the box.
Four quickly became five when Ramsey capped off the scoring two minutes later, latching on to a Sanchez cross before keeping his composure to take the ball past Farman and walk it into the net.
The 9,000 travelling Lincoln fans did almost have something to cheer when Alan Power's curling effort forced a sprawling save from Cech with 10 minutes left, but that was a rare break in the one-way tide and Arsenal were soon back on top looking for a sixth goal.
Sanchez almost got it when he crashed a free kick against the woodwork in the closing stages, while Walcott also fired wide before the referee put Lincoln out of their misery once and for all.
Arsenal, who join Manchester City in the semi-finals of the competition, remain on course to win the trophy for a third time in the last four years, while Lincoln will now turn their attention back to winning promotion from the National League this season.