The 22-year-old opener reached the milestone on 57 and he went on to make 87 to add to his career-best 156 in the first innings.
Fynn Hudson-Prentice helped Haines add 81 for the sixth wicket and scored a half-century, but leg-spinner Luke Hollman followed his five wickets in the first innings by taking five for 90 to finish with career-best match figures of 10 for 155.
Sussex were eventually bowled out for 303, as Middlesex won by an innings and 54 runs and have two wins out of two in Division Three.
The hosts were still 269 runs in arrears at the start and they lost George Garton in the fifth over of the day, when he got a thin edge to wicketkeeper John Simpson pushing forward to Hollman for 17.
Dan Ibrahim (15) looked solid enough until he chipped a tame catch to mid-on to give Hollman another wicket but Haines and Hudson-Prentice, who returned to Sussex from Derbyshire for a second spell last month, added 81 in 24 overs either side of lunch with few alarms.
Hudson-Prentice played some eye-catching drives off both Hollman and the Middlesex seamers and for a while Sussex entertained thoughts of saving the game.
But Haines, who had been on the field for all but 34 balls of the match, not surprisingly tired and on 87 tried to drive Hollman down the ground and Thilan Walallawita made ground to take the catch at long off. Haines had faced 170 balls and hit eight fours, taking his aggregate for the season to 1030 runs at an average of 51.96.
Hudson-Prentice had played very fluently until slow left-armer Walallawita found some extra bounce out of the foot holds and he gloved the ball to Simpson for 67, made from 104 deliveries with nine fours.
Oli Carter and Delray Rawlins added 33 before Middlesex captain Tim Murtagh struck as soon as he took the new ball, tempting Rawlins with a short ball which he obligingly pulled into the hands of Hollman at deep mid-wicket.
Jack Carson (6) lost his off stump to Murtagh’s nip-backer and Martin Andersson picked up the final wicket when he pinned Henry Crocombe for five, leaving Oli Carter unbeaten on 31.
Haines said: "We're disappointed. We genuinely believed when we turned up today that we could get a draw but we didn't bat well enough on the last two days which is disappointing because there was enough skill in our dressing room to have batted through and got the draw.
"There were a few poor shots and lapses in concentration from us. I'm not taking anything away from their bowling but we did give them a few wickets which we didn't need to. Personally, I feel very proud to have reached 1,000 runs because I have worked extremely hard so it's a nice moment for me."