In the Edinburgh club's final friendly before the Betfred Cup starts, teenager Anthony McDonald scored early on against the club where he spent last season on loan. Substitute Mitchell Curry equalised for Inverness as the match entered its closing stages.
Hearts controlled much of the proceedings in front of a 1846 crowd and really ought to have put the game to bed before conceding on 76 minutes. Sterling work by the visiting goalkeeper Mark Ridgers, another former Tynecastle employee, repeatedly denied them.
Beith, 23, was sadly forced to retire from football through injury in April this year. He emerged from the Riccarton youth academy in 2013 and spent last season with Inverness. He now works as a coach with Hearts Under-12s and was given a rousing reception prior to kick-off at Tynecastle.
The Highlanders, managed by the Gorgie legend John Robertson, began this fixture with four former Hearts players in their starting line-up - Ridgers, defender Brad McKay, plus forwards James Keatings and Nikolay Todorov. The hosts were forced into an early change when Craig Wighton trudged off injured to be replaced by teenager Euan Henderson.
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From McDonald's intelligent back-flick, Henderson angled a shot narrowly wide of Ridgers' goal moments after entering the field. McDonald then opened the scoring on 20 minutes following a perfectly-executed set-piece. Oilver Bozanic passed short to Harry Cochrane on the edge of the Inverness penalty area, and he clipped a first-time cross for McDonald to prod home from around six yards.
Dario Zanatta shot into Ridgers' arms on the half-hour with Hearts playing an open, attacking game against opponents from a league below. Henderson then had three outstanding chances in succession but could only watch Ridgers repel them all.
From Christophe Berra's header across goal, the forward's point-blank header was brilliantly parried. The goalkeeper's legs then blocked the forward's shot from McDonald's through pass, and minutes later Henderson fastened on to Steven MacLean's head flick before Ridgers' left hand thwarted his attempted finish.
Inverness struck the crossbar in the last act of the first period as Cochrane miscued a clearance. The second half began after several Hearts substitutions and Todorov saw two efforts sail just over the home goal, now occupied by Zdenek Zlamal. MacLean then had a turn and shot at the opposite end which Ridgers held.
The Inverness keeper continued defying his former club as the match wore on. MacDonald sprinted on to Henderson's threaded ball for a first-time attempt which Ridgers pushed away to his right. He then used both hands to collect Zanatta's rising 20-yard drive.
Keatings found himself with a glaring opportunity to equalise on 68 minutes. However, the striker took a slipped pass from Charlie Trafford and drove it powerfully into Tynecastle's Roseburn Stand. Hearts attacked again as substitute Cammy Logan played a useful one-two with MacLean on the right, but once in on goal he dragged his shot wide of the far post.
Aidan Keena was introduced for Henderson before Inverness forced an equaliser. Keatings' inswinging corner was converted by Curry from close range, and with the scoreline level the game was open for anyone to win.
Ridgers again sprung to his side's rescue by using his fingertips to divert Keena's drive past his right post. That was the final chance of an entertaining 90 minutes aimed at helping young Beith cope after his career ended prematurely.
Hearts (4-4-2): Doyle (Zlamal 46); M Smith (Logan 46), Dikamona, Berra (Petkov 46), Burns; McDonald (Moore 82), Cochrane, Bozanic (Brandon 46), Zanatta (C Smith 82); MacLean, Wighton (Henderson 9 (Keena 73)).
Inverness CT (4-4-2): Ridgers; McKay (Nicolson 80), Donaldson, McCart (White 54), Tremarco (Harper 57); Walsh, Carson, Trafford (Hyde 71), Machado (Curry 57); Todorov, Keatings (MacGregor 80). Unused subs: Mackay, Brown, Chalmers.
Referee: Gavin Duncan.