Hammond nodded home a cross early on from close range to put the home side ahead before Orlandi swung in a free-kick which went through a crowded area to make it 2-0.
Despite the best efforts of the visitors Albion chalked up just their second clean sheet in eight games and picked up three more points.
It was the home side who started the brighter and took an early lead after just six minutes. Will Buckley won a free-kick on the right which was taken short by Orlandi and clipped into the box by Liam Bridcutt for Hammond to head home.
And 20 minutes later Brighton's advantage was doubled from another set-piece. Orlandi's inswinging free-kick caught out Tom Heaton completely and the ball went through the keeper's legs before ending up in the back of the net.
Orlandi, having opened his Seagulls account for the season, then tried his luck with a curling effort from the edge of the box that flew inches past the post.
In the 36th minute City carved out their first real chance of the match when Stephen Pearson, who netted in Saturday's victory, crashed a left-footed effort off Tomasz Kuszczak's crossbar from 20 yards out after being teed up by Marvin Elliott.
Just four minutes later Derek McInnes' men had another big chance to get back into the match but Neil Danns' effort was cleared off the line by Gordon Greer after the Leicester loanee was picked out at the back post. And when the ball fell back to Danns again he was denied by Kuszczak.
Brighton started the second half as they had the first and created two great chances shortly after the break.
First Will Hoskins nodded Buckley's ball down to Orlandi who fired over before Hoskins ran onto Dobbie's throughball and his low shot was kept out by Heaton.
City continued to pile on the pressure as they looked for just their third away win of the season with Albert Adomah and Neil Kilkenny both trying their luck from long-range but to no avail.
Hoskins, making his first start for the club since January, had the Seagulls' next chance at the end of a flowing move with an acrobatic effort in the 76th minute which was well blocked by Bates.
The 395 travelling fans almost had a late goal to cheer about but half-time substitute Ryan Taylor headed Kilkenny's cross wide.