Rain and bad light at either end of the day at Hove restricted the day's allocation to 42 overs and Yorkshire's hopes of making further inroads into leaders Durham's advantage at the top of Division One suffered.
Left-armer Zaidi, Pakistan-born but now English-qualified and playing his first first-class game for nearly four years, finished with four wickets for 57 runs as Yorkshire lost their last six men for 76.
Bowled out for 326, the visitors held a lead of 34, which turned into a 14-run deficit as Sussex reached 48 for two when bad light ended play.
Durham's hopes of boosting their title challenge by winning at Derby for the first time were frustrated by a combination of accurate Derbyshire bowling and bad weather.
The leaders closed 41 runs behind on 257 for four when rain ended play early. Scott Borthwick (89) and Will Smith (81) shared a third-wicket stand of 159 in 62 overs but Derbyshire kept them in check and the game now looks to be heading for a draw.
Lewis Gregory and Peter Trego struck twice each as Somerset strengthened their grip on the relegation clash with Surrey at Taunton.
But, to the frustration of the home side, rain allowed only 29.2 overs on day three and they now face a race against time to press home their advantage, with Surrey 97 for four in their second innings, a lead of 32.
The third day of the match between third-placed Middlesex and fourth-from-bottom Nottinghamshire at Lord's was called off without a ball being bowled.
In Division Two, Lancashire and Leicestershire were frustrated by the weather as only 40 overs were possible on day three at Old Trafford.
When the rain arrived at 2pm, the bottom county were 60 for three from 22 overs in reply to Lancashire's 453 for seven declared in their first innings.
Lancashire's title rivals, Essex, were another side frustrated by the weather - rain led to the loss of 63 overs on day three as they pushed for victory over Kent at Canterbury.
Sam Northeast's unbeaten 70 enabled the hosts to take the game into the final day, although they remain 56 runs in arrears on 113 for four second time around.
Discarded England spinner Monty Panesar grabbed three of the wickets for the promotion-chasing visitors, at a cost of 24 runs in 11 overs.
Hampshire made the most of the 90 minutes of play possible on the third day of their rain-interrupted match at Worcestershire.
James Tomlinson took two wickets, while Matt Coles took the other to fall as the home side reached 189 for five in their struggle to avoid the follow-on, replying to Hampshire's 428.