Sussex 319 for 4 (Alsop 118*) vs Leicestershire
Australia's chief batting hope to face England this summer, who made a low-key 30 on his Sussex debut at Worcester last week, was back in the pavilion after facing just 14 balls, dismissed leg before wicket by South African seamer Wiaan Mulder for three.
Smith, who is halfway through a three-match sojourn with the Division Two side, had spent Thursday ensconced in the dressing room as Leicestershire's groundstaff tried in vain to make a saturated outfield fit for play.
Alsop, the 27-year-old left-hander, went on to complete his ninth first-class century in an unbroken stand of 121 with 19-year-old all-rounder James Coles, who is unbeaten on 59. Mulder has figures of three for 52 from 20 overs.
Despite Smith's flop, Sussex should be delighted with their day after being asked to bat first in challenging conditions.
How they fare with the ball remains to be seen given that England's Ollie Robinson is rested and the Australian quick, Nathan McAndrew - their joint leading wicket-taker with Robinson - has had to step aside to accommodate Smith.
On a pitch with a good covering of grass, Sussex had been two-down for 91 at lunch after a session played with a chilly wind whipping across the large playing area at Grace Road and the sky uniformly grey.
Leicestershire, who dropped the out-of-form Mikey Finan from their seam attack and brought in Will Davis for his first Championship action since June last year, initially struggled to contain the Sussex openers but first change Mulder struck twice in his opening spell.
The all-rounder, presented with his county cap during the course of the playless opening day, found the inside edge of Tom Clark's bat in his second over and followed up by trapping Ali Orr leg before with one that struck him at shin height.
But Pujara drew on his deep reserve of experience to frustrate the Leicestershire bowlers, never losing his patience while the going was tough, safe in the knowledge that scoring opportunities would come.
The qualities rubbed off on Alsop, who reached his half-century from 126 balls when he drove Chris Wright square of the wicket for his ninth boundary. Alsop made 150 and 60 not out when the sides met at Hove last season, although ultimately eclipsed by double-hundreds from both Mulder and Colin Ackermann in a run-heavy draw.
Pujara dealt largely in boundaries, 11 of them in his first 50 (from 113 balls), which he reached by hammering Ackermann's off-spin through midwicket, the first of three in a row in an over that cost 15 runs. Three more boundaries in Ackermann's next (and last) over - two of them to Pujara - prompted a reminder that the Indian maestro had passed fifty eight times previously for Sussex and never failed to make 100.
It appeared this innings would follow a similar pattern. Seemingly in the blink of an eye, Pujara moved on to 77 and the only moment of obvious good fortune had been an edge off the unlucky Davis that flew between 'keeper Peter Handscomb and a solitary, wide slip.
But then it was over. Tom Scriven, generally tidy albeit cut easily for a 16th four by Pujara the ball prior to his dismissal, bowled the next one straighter and Pujara misjudged it enough to tickle an inside edge on to pad, the ball looping to Handscomb. It was the 24-year-old seamer's 12th first-class wicket, easily his most satisfying.
Pujara's departure ushered in Smith, but any expectation that Australia's No. 1 batsman could trump his likely opponent in next month's World Test Championship final soon evaporated. Smith looked twitchy from the start, surviving a confident appeal for leg before by the eager Scriven from his second ball faced, offering no shot.
It appeared only height could have saved him. There was no such doubt three overs later when he shuffled into a ball from Mulder that came back in a little and would certainly have hit. Sussex were well placed on 208 for four at tea, but walked off to a sense of anticlimax.
The final session, which would have lasted a marathon 39 overs had bad light not curtailed play 13 overs before the scheduled close, saw Alsop complete a 212-ball century when he cut the occasional spin of Sol Budinger for his 14th four before Leicestershire took the second new ball and Coles go to his fourth first-class fifty from 69 balls, with seven fours and a pulled six off Scriven.